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Journal Cover Research & Reviews : Journal of Statistics
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   Full-text available via subscription Subscription journal
   ISSN (Print) 2348-7909 - ISSN (Online) 2278-2273
   Published by STM Journals Homepage  [67 journals]
  • Average Number of Real Zeros of a Random Trigonometric Polynomial with
           Cauchy Distributed Coefficients
    • Authors: S. Bagh
      Abstract: Abstract be a random trigonometric polynomial where the coefficients ak’s (k=1, 2, ..., n) are independent Cauchy distributed random variables and Nn(w) be the number of real zeros of T(q), 0≤q≤2p, then it is proved that the average number of real zeros of the trigonometric polynomial T(q) in the interval (0, 2p) is given by ENn=O(n). Keywords: Random trigonometric polynomial, Cauchy distribution, characteristic function, Kac-rice formulaCite this Article Bagh S. Average Number of Real Zeros of a Random Trigonometric Polynomial with Cauchy Distributed Coefficients. Research & Reviews: Journal of Statistics. 2016; 5(2): 62–70p.
         be  a random trigonometric polynomial where the coefficients ak’s (k = 1,2,..., n) are independent Cauchy distributed random variables and Nn(w) be the number of real zeros of T(q), 0 ≤ q ≤ 2p, then it is proved that the average number of real zeros of the trigonometric polynomial T(q) in the interval (0,2p) is given by ENn = O(n).
      PubDate: 2016-08-09
      Issue No: Vol. 5 (2016)
  • An Anthology of Parametric ROC Models
    • Authors: S. Balaswamy, R. Vishnu Vardhan
      Abstract: In the context of classification problems, ROC curve has gained its importance in classified fields. The so called parametric form of ROC curve, namely, Binormal ROC model was developed by assuming normal distributions. However, the practical situations in classifying individuals/objects demanded new forms of ROC models. The present paper brings out an insight into the theoretical development of different parametric forms of ROC models and its measures. Keywords: AUC, Binormal ROC curve, Hybrid ROC curves, KLD and Optimal ThresholdCite this Article S. Balaswamy, R. Vishnu Vardhan. An Anthology of Parametric ROC Models. Research & Reviews: Journal of Statistics. 2016; 5(2): 32–46p.
      PubDate: 2016-08-07
      Issue No: Vol. 5 (2016)
  • Determinants of Rural-Urban Migration in Bangladesh including its
           Consequences for Origin Households and Urban Amenities
    • Authors: Md. Zakir Hossain, Md. Ohidul Alam Khan, Jasim Uddin Ahmed
      Abstract: Rural-urban migration mainly contributes to urban growth in the developing countries and accounts for about two-thirds of the urban growth in Bangladesh since independence. In the twentieth century, the urban population in Bangladesh increased about forty-fold in contrast with four-fold for rural population. Owing to limited opportunities in the rural areas, a large number of people continue to move towards towns/cities for their livelihood. The objective of the paper is to identify the determinants of rural-urban migration and its consequences for origin and destination to formulate appropriate strategies to reduce the adverse impacts of undue inflow of migration. The study has adopted household level survey at origin and individual level interview at destination to collect the desired data and information on 480 migrant and 210 non-migrant households from 30 clusters of Bangladesh financed by social science research council (SSRC) of planning commission, Bangladesh. The rural-urban migration rate from different mauzas/villages is estimated at 10.31%. The multiple binary logistic regression analysis has identified that maximum educational level of the household, occupation of the household head, landholding, number of adult male members and dependency ratio are the significant determinants of rural-urban migration. The likelihood of rural-urban migration is documented higher for the households whose members attained at least primary level of education; whose heads’ occupations were service, non-agricultural labor and unemployment; and who stay at the both ends of the landholding ladder. Regarding the consequences at the place of origin, the study has explored that rural-urban migration puts a significant and positive impact on the migrant households as a livelihood strategy. Apart from the rapid urbanization, the rural-urban migration reduces urban amenities impinging overwhelming population pressure. A vast majority of the migrants agreed with the decreasing trend of urban amenities as an adverse affect of migration, and the major problematic areas of urban amenities are identified as electricity, housing, transportation and gas. To optimize the rural-urban migration and its outcome, the study suggests some policy implications that include increasing the education facilities in the rural areas, taking proper steps to encourage the natural calamities refugee migrants for rural-rural migration instead of rural-urban migration; decentralizing the administration, industrialization, and commercialization to minimize the untoward rural-urban migration flow. Keywords: Rural-urban, migration, livelihood, regression analysisCite this Article Md. Zakir Hossain, Md. Ohidul Alam Khan, Jasim Uddin Ahmed. Determinants of Rural-Urban Migration in Bangladesh including its Consequences for Origin Households and Urban Amenities. Research & Reviews: Journal of Statistics. 2016; 5(2): 47–61p.
      PubDate: 2016-08-07
      Issue No: Vol. 5 (2016)
  • Graph Sampling by Spanning Tree under Stratified Setup
    • Authors: Diwakar Shukla, Sharad Pathak, Shashikant Trivedi
      Abstract: The sampling theory and its methodologies are based on assumption that the population under survey is of individuals and respondents have provided the answer of questions asked. When population is of graphical structure like containing nodes and edge links then it is complicated to apply the usual sampling procedures. Spanning tree is specified type of a graph, which is always connected with all nodes and becomes a sub-graph. Assume that there are several strata each having structure of graphical population of node-links, each contains graph like spanning tree. A sample containing different size from each stratum is drawn randomly. This paper presents a node-sampling procedure to draw sample and estimate the population mean-edge-length in the setup of stratified graphical structured population of spanning tree. An estimation procedure is suggested and expressions of mean squared error are obtained. Optimum choice of estimator parameter is obtained showing the control over bias as well as mean squared error both. A numerical case in point is given to support of theoretical findings. It is found that node-sampling procedure is worthwhile in stratified population structure. AMS Subject Classification: 62D99, 62-07 and 62-09 Keywords: Spanning Tree, Node-Sampling Procedure, Bias, Mean Squared ErrorCite this Article Diwakar Shukla, Sharad Pathak, Shashikant Trivedi. Graph Sampling by Spanning Tree under Stratified Setup.Research & Reviews: Journal of Statistics. 2016; 5(2): 11–31p.
      PubDate: 2016-07-26
      Issue No: Vol. 5 (2016)
  • Modified Unit Root Test in a Random Effect Panel Data Model under
           Restricted Alternatives
    • Authors: N. Salma, M.F. B. Karim, F. Duty, A. K. Majumder
      Abstract: Many econometric including time series as well as panel data models provide us with prior information about some or all of their unknown parameters. Such information usually comes from economic theory, from previous empirical studies or from functional considerations such as variances always being nonnegative. For this reason, many econometric testing problems are potentially either strictly one-sided or partially one-sided. Since panel data is the combination of time series and cross-sectional data, so autocorrelation problem likely to be occurring in panel data along with nonstationary problem. It needs to be tested. But testing unit root by existing tests did not incorporate the prior information, which provides us inefficient estimate along with low power. In this study, we tried to overcome these problems by using constraint optimization technique of estimation and modifying the unconstraint panel unit root tests. Monte Carlo results show that our proposed tests have good size and power under restricted hypotheses. Keywords: Panel unit root, Constraint-based Test, Random walk, Levin and Lin test, IM, Pesaran and Shin testCite this Article N. Salma, M.F.B. Karim, F.A. Duti  et al. Modified Unit Root Test in a Random Effect Panel Data Model under Restricted Alternatives. Research & Reviews: Journal of Statistics. 2016; 5(2): 1–10p.
      PubDate: 2016-06-29
      Issue No: Vol. 5 (2016)
  • Ageing Classes in Discrete Time Based on Hazard Rate: A Review and New
    • Authors: P. G. Sankaran, Nidhi P Ramesh, N. Unnikrishnan Nair
      Abstract: In the present paper, we review and study different ageing classes for discrete lifetime data using hazard rates. They give us an indication of the pattern of failure of the systems. We discuss four major ageing classes viz. monotone hazard rate class, increasing (decreasing) hazard rate of order 2 class, increasing (decreasing) hazard rate average class and new better used in hazard rate. The interrelationships among these classes are also studied. The odds function in discrete set up is employed to characterize monotone hazard rate classes. These ageing classes are related to various well known stochastic orders. The properties and applications of these classes are discussed. Keywords: Ageing, hazard, discrete, monotoneCite this Article Sankaran PG, Ramesh Nidhi P, Unnikrishnan Nair N. Ageing Classes in Discrete Time Based on Hazard Rate: A Review and New Results. Research & Reviews: Journal of Statistics. 2016; 5(1): 10–26p.

      PubDate: 2016-05-17
      Issue No: Vol. 5 (2016)
  • Entropy and Noiseless Coding Theorem
    • Authors: Sandeep Kaur, Sukhjeet Singh
      Abstract: This paper makes utilization of Kraft's inequality in unique to demonstrate quiet coding hypotheses. In coding hypothesis, we examine different properties of codes for application in information pressure, cryptography, mistake revision, and system coding. The investigation of codes is presented in information theory, electrical designing, arithmetic, and PC sciences for the transmission of information through solid and productive strategies. We need to consider how coding of messages should be possible proficiently so that the greatest number of messages can be sent over a silent divert in a given time. Along these lines, the base estimation of mean codeword length subject to a given limitation on codeword lengths must be established. This paper introduces mean codeword length of order and type for 1:1 codes and analyzed the relationship between average codeword length and fuzzy information measures for binary 1:1 codes. Further, noiseless coding theorem associated with fuzzy information measure has been established. Keywords: Noiseless coding, entropy, Kraft’s inequalityCite this Article Sandeep Kaur, Sukhjeet Singh. Entropy and Noiseless Coding Theorem. Research & Reviews: Journal of Statistics. 2016; 5(1): 27–32p.
      PubDate: 2016-05-17
      Issue No: Vol. 5 (2016)
  • Odds Generalized Exponential Uniform Distribution and its Application
    • Authors: Sudhansu S. Maiti, Sukanta Pramanik
      Abstract: A new distribution, called Odds generalized exponential uniform distribution (OGEUD) is proposed for modeling lifetime data. A comprehensive account of the mathematical properties of the new distribution including estimation and simulation issues is presented. A data set has been analyzed to illustrate its applicability. Keywords: Exponential distribution, maximum likelihood estimation, Odds function, T-X family of distributions, reliability propertiesCite this Article Maiti Sudhansu S, Sukanta Pramanik. Odds Generalized Exponential Uniform Distribution and its Application. Research & Reviews: Journal of Statistics. 2016; 5(1): 33–45p.
      PubDate: 2016-05-17
      Issue No: Vol. 5 (2016)
  • Statistical Methods for Clinical Trials: A Review
    • Authors: Kriti Gupta, Isha Chandra
      Abstract: Clinical trials are used to develop and test interventions in nearly all areas of medicine and public health. In many countries, approval for marketing new drugs hinges on efficacy and safety results from clinical trials. Similar requirements exist for the marketing of vaccines. The randomized clinical trial is widely viewed to be the gold standard for evaluation of treatments, diagnostic procedures, or disease screening. The proper design and analysis of a clinical trial requires careful consideration of the study objectives whether to demonstrate treatment superiority and the nature of the primary end point. Different statistical methods apply when the end point variable is discrete, continuous, or time to event. Other complicating factors include patient noncompliance, loss to follow-up, missing data, and multiple comparisons when more than two treatments are evaluated in the same study. This article provides an overview of the basic statistical approaches for analyzing clinical trials with binary, continuous or time-to-event outcomes as well as methods for handling protocol deviations due to noncompliance and early drop-out. Issues surrounding the determination of sample size and power of clinical trials are also discussed. Subgroup analyses are common in randomised controlled trials (RCTs). There are many easily accessible guidelines on the selection and analysis of subgroups but the key messages do not seem to be universally accepted and inappropriate analyses continue to appear in the literature. This has potentially serious implications because erroneous identification of differential subgroup effects may lead to inappropriate provision or withholding of treatment. Keywords: Clinical, statistical, drug, FDACite this Article Kriti Gupta, Isha Chandra. Statistical Methods for Clinical Trials: A Review. Research & Reviews: Journal of Statistics. 2016; 5(1): 5–9p.
      PubDate: 2016-05-11
      Issue No: Vol. 5 (2016)
  • Recent Trends and Advances in Biostatistics
    • Authors: Richa Chaudhary, Saba Ansari, Isha Chanda
      Abstract: Biostatistics is that subdivision of statistics which is responsible for the appropriate elucidation of scientific facts and figures produced in biology, and other biological and health science related researches and studies. The review discusses and focuses on the applications of biostatistics, computational tools used in the biostatistical calculations and the trends and advancements in the field of biostatistics. Keywords: Biostatistics, computational tools, genetic sequencing, pathwaysCite this Article Richa Chaudhary, Saba Ansari, Isha Chandra. Recent Trends and Advances in Biostatistics. Research & Reviews: Journal of Statistics. 2016; 5(1): 1–4p.
      PubDate: 2016-05-10
      Issue No: Vol. 5 (2016)
  • A Density Version of A Local Limit Theorem for Properly Normalised
           Weighted Sums
    • Authors: KN Raviprakash, K Vidyalaxmi, Gooty Divanji
      Abstract: Let be a sequence of i.i.d. random variables with a common distribution function F with. Let  and, where f is positive, non - decreasing and continuous on [0,1] with . Let  be an integer sequence such that, , where  and are sequences of norming constants with as . We obtain a moment convergence result for and a density version of a local limit theorem when distribution function F belongs to the domain of partial attraction of a semistable law. Keywords and Phrases: Limit distribution, Domain of partial attraction, Moment convergence, Local limit theorem.Cite this Article KN Raviprakash, K Vidyalaxmi, Gooty Divanji. A density version of a local limit theorem for properly normalised weighted sums. Research & Reviews: Journal of Statistics. 2015; 4(3): 29–37p.

      PubDate: 2015-12-28
      Issue No: Vol. 4 (2015)
  • A Review on Statistical Analysis Correlation and Regression
    • Authors: Richa Chaudhary, Isha Chandra, Saba Ansari
      Abstract: In statistics, dependence is any applied mathematics relationship between two random variables or two sets of information. Correlation refers to any of a broad category of applied mathematics relationships involving dependence; acquainted samples of dependent phenomena embrace the correlation between the physical statures of oldsters and their offspring, and therefore the correlation between the demand for a product and its worth. Keywords: Correlation, Regression, Multiple Linear Regression, VariablesCite this Article Chaudhary et al. A review on statistical analysis correlation and regression. Research & Reviews: Journal of Statistics. 2015; 4(3): 14–18p.
      PubDate: 2015-12-28
      Issue No: Vol. 4 (2015)
  • An Extensive Review on Statistics
    • Authors: Ashutosh Awasthi, Asit Srivastava
      Abstract: When a census is not possible a selected set of the population known as a sample is studied. Once a sample that is representative of the population is decided, information is collected for the sample members in a data-base or experimental setting. Again, descriptive statistics may be accustomed to summarize the sample information. However, the drawing of the sample has been subject to a component of randomness, therefore the established numerical descriptors from the sample are also because of uncertainty. Still, to draw purposeful conclusions regarding the whole population, inferential statistics is required. It uses patterns within the sample information to draw inferences regarding the population depicted, accounting for randomness. These inferences might take the shape of respondent yes or no questions about the information hypothesis testing, estimating numerical characteristics of the information estimation, describing associations at intervals, the information correlation and modeling relationships at intervals of the information. Reasoning will extend to forecasting, prediction and estimation of unobserved values either in or related to the population being studied; it will embody extrapolation and interpolation of your time series or abstract information, and may conjointly embody data processing. Keywords: Population, analysis, mathematics, null hypothesisCite this Article Ashutosh Awasthi, Asit Srivastava. An extensive review on statistics. Research & Reviews: Journal of Statistics. 2015; 4(3): 19–28p.
      PubDate: 2015-12-28
      Issue No: Vol. 4 (2015)
  • Determinants of Under-Five Mortality by Using Multivariate Proportional
           Hazard Model: A Case Study in Bangladesh
    • Authors: Suman Biswas, Md. Yasin Ali Parh
      Abstract: Bangladesh wants to achieve the millennium development goals which is related to infant and under-five mortality by the year 2015. To achieve the goals it is needed to reduce the child mortality and to reduce mortality in Bangladesh it is needed to determine the determinants of mortality. Thus, the main purpose of this study is to find the determinants of under-five mortality in Bangladesh. The objective of this study is to determine the impact of parental, socioeconomic, demographic, environmental, and nutritional and health seeking variables on under-five mortality. This study used the data extracted from Bangladesh demographic and health survey (BDHS). Chi-square test for dependency checking and multivariate proportional hazard analysis techniques are used to investigate the effects of those variables on under-five mortality. The study results show that several socioeconomic, demographic, nutritional, environmental and health related variables effect on under-five mortality. Multivariate hazards analysis results show that father’s education, region of residence, preceding birth interval, number of children under-five years of age, mother’s age, contraceptive use and breastfeeding have significant effect on under-five mortality. In this study it has revealed that the environmental, demographic, nutritional and health seeking variables have highly significant impact on under-five mortality than the socioeconomic variables. Therefore, we should give attention to these influencing variables to reduce the rate of under-five mortality in Bangladesh. Keywords: Under-five mortality, bivariate analysis, multivariate proportional hazard, relative risk (odds ratio), determinantsCite this Article Suman Biswas, Md. Yasin Ali Parh. Determinants of Under-Five Mortality by Using Multivariate Proportional Hazard Model: A Case Study of Bangladesh. Research & Reviews: Journal of Statistics. 2015; 4(3): 1–13p.

      PubDate: 2015-12-04
      Issue No: Vol. 4 (2015)
  • Effect of Imprecisely Specified Life Style Factors on Gallbladder
           Carcinoma: A Simple Bayes Study
    • Authors: Richa Srivastava, S. K. Upadhyay, V. K. Shukla
      Abstract: Medical data are often not available in a clear form for the routine implementation of statistical techniques. The paper considers one such imprecisely specified data on two life style factors to examine if the same can be considered as causal factors for the development of gallbladder carcinoma. The modelling formulation is based on the multivariate-Dirichlet combination with imprecisely specified factors treated as further unknowns in the Bayesian implementation. The prior hyperparameters are chosen in two ways based on either arbitrary choices leading to vague prior consideration or on empirical Bayes formulation. The results are illustrated on the basis of a real data example. Keywords: Imprecise data, gallbladder carcinoma, multinomial‐Dirichlet formulation, life style factors, vague prior, empirical Bayes.
      PubDate: 2015-12-04
      Issue No: Vol. 4 (2015)
  • Evaluation of Skip-Lot Sampling Inspection Plans by Attributes Based on
           Bayesian Methodology
    • Authors: D. Rajalakshmi, R. Vijayaraghavan, A. Loganathan
      Abstract: Skip-lot sampling is a system of lot-by-lot sampling inspection plans in which a provision is made for skipping inspection of some of the submitted lots when the quality of the submitted product is good. The plans under the system are generally viewed as an extension of continuous sampling to lots. A specific skip-lot plan under its operation uses a given lot inspection plan by the method of attributes called the reference sampling plan. An implicit assumption underlying such procedures by attributes is that the lot or process fraction nonconforming is a constant. This assumption is not fulfilled markedly, even if the production process is stable, that is, if the probability of observing a nonconforming unit is a constant. In such cases, Bayesian methodology which utilizes prior information on the process variation for taking decisions about the submitted lots can be used under skip-lot plans as an alternative to the conventional approach. This paper presents the concept of Bayesian skip-lot sampling with a zero acceptance number single sampling plan as the reference plan and its operating characteristic function under the conditions of Polya distribution. The empirical properties of operating characteristic curves of such plans for varying sets of parameters are highlighted. An iterative procedure for selecting the plans providing protection to the producer and the consumer with reference to two prescribed points on the OC curve is developed. Keywords: Lot-by-lot sampling plan, fraction nonconforming, operating characteristic function, Polya distribution, skip-lot sampling plan, single sampling plan
      PubDate: 2015-12-03
      Issue No: Vol. 4 (2015)
  • An Application of Gamma- Poisson Hierarchical Model for Modelling Failure
           to Operation Points for a Canning Process
    • Authors: Ram Prasad Khatiwada
      Abstract: Standard statistical methods are required for detecting Critical Control Points (CCPs) when Hazard Analysis and Critical Control Points (HACCP) system is put into practice for the identification, evaluation and controlling food safety hazards. The common practice for this problem is to select CCPs by simply observing the phenomena. This work emphasizes the use of data-based information to the CCP procedure, where loss of control may result in an unacceptable product. It presents the method of obtaining posterior estimates for the failure-rate to operation points. The work considers the gamma-Poisson based hierarchical structuring for identifying and modelling critical points for the failure to different operation points of canning in a fruit juice industry. Both real and simulated data sets are considered to validate and demonstrate the proposed method using WinBUGS software.  The performance of the proposed estimators is also studied. Keywords: HACCP, gamma-Poisson hierarchical model, failure rate, food safety hazard, critical points
      PubDate: 2015-12-03
      Issue No: Vol. 4 (2015)
  • A Study on the Construction and Selection of Bayesian Reliability Sampling
           Plans under the Conditions of Exponential Distribution
    • Authors: A. Loganathan
      Abstract: In reliability sampling plans, decision on the submitted lots is taken based on the information obtained from a life test. In many cases of reliability studies exponential distribution is used as the probability model of the lifetime of the products. When the products have minimum lifetime, two-parameter exponential distribution would be more suitable.  In this paper, life test based single sampling plans are designed in the Bayesian approach under hybrid censoring scheme assuming that the lifetime is distributed according to a two-parameter exponential distribution. Employing natural conjugate prior to the model parameters, the predictive distribution of the lifetime is derived. Plan parameters are obtained satisfying two points on the operating characteristic curve. Selection of the plan parameters is described with numerical illustrations. Keywords: Reliability sampling plan; life test; natural conjugate prior; operating  characteristic function; producer’s risk; consumer’s risk.
      PubDate: 2015-12-03
      Issue No: Vol. 4 (2015)
  • Comparison of Some Estimators under Second Order Approximation
    • Authors: Prayas Sharma, Rajesh Singh
      Abstract: Many researchers [1–5] proposed estimators for estimating population mean .  Up to the first order of approximation and under optimum conditions, the minimum mean squared error (MSE) of all the above estimators is equal to the MSE of the regression estimator. In this paper, we have tried to found out the second order biases and mean square errors of these estimators using information on auxiliary variable based on simple random sampling.  Finally, we have compared the performance of these estimators with some numerical illustration. Keywords: Simple Random Sampling, population mean, study variable, auxiliary variable, exponential ratio type estimator, exponential product estimator, Bias and MSE. 
      PubDate: 2015-12-03
      Issue No: Vol. 4 (2015)
  • The Changing Trends and Levels in Fertility with Respect to Several
           Factors: A Case Study of Rural Areas of Pauri Garhwal in Uttarakhand
    • Authors: Pankaj Bahuguna, O. K. Belwal
      Abstract: This paper addresses the issue of fertility impacts on several factors in Uttarakhand. Status of women in any society is a significant pointer to the standard of that society. In all societies women not only give birth to children, but perform also childcare. Therefore, circumstances of high fertility tend to lock them up within the domestic domain. In recent times there are some changes in trends and levels of fertility. Measures of gender equality tend to be greatest in societies with low fertility. Recent decades have seen women becoming more like men with respect to levels of education, employment patterns and social status. Fertility rates fall and differences between rich and poor narrow as both groups converge on having smaller families. In this study of fertility trends, the demand for children, and the position of women in their socio-cultural contexts, the family welfare programme and its limitations are considered.  The analysis demonstrates that literacy, per capita income, child survival, use of contraceptives use, the fall in the number of children desired and women's status are responsible for declining trends and levels of fertility. The main factor is rural-urban migration to perform more effective role in reducing fertility levels. This is a case study of Pauri Garhwal. Keywords: Demography, women’s status, fertility levels, migration, gender equality, rich and poor.
      PubDate: 2015-12-03
      Issue No: Vol. 4 (2015)
  • Determination of Bayesian Life Test Sampling Plans Based on Maxwell -
           Square Root Inverted Gamma Distribution
    • Authors: P. Muthu Krishnan, A. Loganathan, S. Mari Chelvi
      Abstract: Reliability sampling plans are used in industries to take decisions on the disposition of lots when lifetime is the quality characteristic. Various censoring schemes are adopted in life tests conducted to assess the lifetime of the sampled products in order to save time and cost.  When the quality of products vary over lots, incorporation of such information would give better sampling plans. In this paper, determination of reliability sampling plans is studied in the Bayesian approach assuming that the distribution of the lifetime is Maxwell distribution. Square root inverted gamma prior distribution is employed to the parameter in the Maxwell distribution. The sampling plans are determined under hybrid censoring scheme using hypergeometric probabilities. The sampling plans protect the interests of both producer as well as consumer.  Selection of sampling plans is illustrated through numerical examples.   Keywords: Reliability sampling plan, Maxwell distribution, square root inverted gamma distribution, operating characteristic function, life test, producer’s risk, consumer’s risk.  
      PubDate: 2015-12-03
      Issue No: Vol. 4 (2015)
  • Bayesian Modified Chain Sampling Plan
    • Authors: H. Akamanchi Raghottam, J. Jothikumar
      Abstract: Chain sampling plan (ChSP-1) is a sampling plan applicable in situations involving small samples and costly or destructive testing and replaces zero acceptance number single sampling plans.  The current lot is accepted under ChSP-1 if the samples from the previous consecutive lots do not have nonconforming products and the sample from the current lot has one or no nonconforming product.  Though the operating characteristic curve of ChSP-1 discriminates the lots of good and poor quality lot well, the plan does not help to reduce the sample size. The modified chain sampling plan (MChSP-1) was proposed with a modification in chaining the results of the previous consecutive results in order to obtain plan with smaller sample size than ChSP-1.  This paper discusses the MChSP-1 in the Bayesian approach, employing gamma prior distribution to the parameter in the Poisson distribution.  The operating characteristic function, a measure of performance of sampling plans, of the Bayesian modified chain sampling plan is derived.  Properties of the operating characteristic function are studied using empirical results. Keywords: Operating characteristic (OC) function, probability of acceptance(pa), modified chain sampling plan (MChSP-1), Bayesian modified chain sampling plan (BMChSP-1) 
      PubDate: 2015-12-03
      Issue No: Vol. 4 (2015)
  • Designing Re-sampling Schemes using Bayesian Methodology
    • Authors: K. Rajagopal, R. Vijayaraghavan, A. Loganathan
      Abstract: When the quality of the finished products of a production process is near perfect and the randomness of the samples is in question or the test procedures may not be accurate, re-sampling schemes are the suitable acceptance sampling plans.  In the re-sampling schemes, re-submission of lots (which are not accepted) is allowed, if the provisions of the statute permit. Such re-sampling schemes provide better protection to producer without compromising the protection to the consumer, and are (considered) more suitable ‘special sampling plans’. These schemes should be developed and designed based on the Bayesian methodology, particularly when the between-lot quality variation is more than the within-lot quality variation.  A true assessment of the sampling risks could be made by applying this methodology while designing such sampling schemes. In this paper, a re-sampling scheme is developed based on the predictive distribution of the lot quality which is a random variable, in association with the sampling distribution. The advantage of the developed sampling plan is also presented in the paper.   Keywords: Operating characteristic function, predictive distribution, re-submitted lots, sampling inspection plan and sampling risks.
      PubDate: 2015-12-03
      Issue No: Vol. 4 (2015)
  • Hybrid Bernoulli-Triangular Distribution
    • Authors: B. Ramya, S. Sampath
      Abstract: Chance theory deals with environments where both randomness and fuzziness coexist. This paper considers the development of a new hybrid distribution called “Bernouli-Triangular” distribution which treats the parameter involved in classical Bernouli distribution as a triangular fuzzy variable. Theoretical expressions for Chance distribution, its mean and variance are derived for various cases arising in the hybrid distribution developed in this work. It was noticed that the expressions for mean and variance of the hybrid Bernouli-Triangular distribution resemble those corresponding to Bernouli probability distribution.Keywords: Chance measure, hybrid variable, hybrid Bernouli-Triangular distribution, chance distribution, expected value, varianceCite this Article: Ramya B, Sampath S, Hybrid Bernoulli-Triangular Distribution. Research & Reviews: Journal of Statistics. 2015; 4(1): 8–19p.
      PubDate: 2015-04-27
      Issue No: Vol. 4 (2015)
  • Probabilistic Approach to Explore Indian Population Trends
    • Authors: Kumari Shivangi, Harinarayan Tiwari, Randhir Kumar Chaudhary
      Abstract: This paper presents a stochastic description of the total population (census data) of India. An estimate to their distribution can be obtained using three non-linear distributions; Beta, Johnson SB & Power Function. Total population of India have a quadratic polynomial trend and best fitted with Johnson SB distribution. Beta and power function distribution both under predict the maximum value and over predict the minimum value. Johnson SB distribution over predicts the maximum value and under predicts the minimum value so it can nearby range of population that lies between the distributions. It also provides new approach to think for population forecasting.Keywords: India, population, probability, beta distribution, census, power functionCite this Article: Kumari Shivangi, Harinarayan Tiwari, Randhir Kumar Chaudhary. Probabilistic approach to explore Indian population trends. Research & Reviews: Journal of Statistics. 2015; 4(1): 20–25p.
      PubDate: 2015-04-27
      Issue No: Vol. 4 (2015)
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