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Journal Cover   Research & Reviews : Journal of Statistics
   Full-text available via subscription Subscription journal
   ISSN (Print) 2348-7909 - ISSN (Online) 2278-2273
   Published by STM Journals Homepage  [61 journals]
  • 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)
  • On Estimation of R=P for Birnbaum-Saunders Distribution
    • Authors: Shayla Naznin, Md. Soyebur Rahman
      Abstract: On Estimation of R=P(Y<X) for Birnbaum-Saunders DistributionIn this paper the estimation of R=P(Y<X) is performed. Where Y and X are two independent Birnbaum-Saunders distribution, when Y is stress and X is strength. Monte-Carlo simulation is performed to obtain the estimate of R. The MLE of the R is obtained from iterative method.Keywords- Stress-Strength model, maximum likelihood estimator, stress, strength, reliabilityCite this Article: Shayla Naznin, Md. Soyebur Rahman. On Estimation of R=P(Y<X) for Birnbaum-Saunders Distribution. Research & Reviews: Journal of Statistics. 2015; 4(1): 1–7p.
      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)
  • 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: 2015-01-05
      Issue No: Vol. 3 (2015)
  • Determinants of Age at First Marriage and Its Influence on Completed
    • Authors: Gowranga Kumar Paul, Shayla Naznin, Mashfiqul Huq Chowdhury, Deluar J. Moloy
      Abstract: Early marriage is highly prevalent in Bangladesh. Early marriage tends to increased fertility resulting in high population growth. It is important to identify the various social and cultural factors influencing age at first marriage as well as completed fertility. The purpose of this study is to identify the factors that have some contributions to raise the age at marriage of females vis-a-vis fertility decline in two different periods using the data from Bangladesh Demographic and Health Survey (BDHS) 2007. Descriptive statistics have been used to describe the distribution for background characteristics of the couples. Poisson regression model has been employed to study the impact of several covariates on completed fertility. The study tends to confirm that overall mean age at first` marriage of rural Bangladeshi woman is only about 15 years. Marriage cohort analysis of the respondents suggests that mean age at first marriage among most recent cohort is more than 1 year higher compared to the cohort that completed their reproductive age. Independent χ2-test statistic reveals that respondent’s education, access to mass media, religion, husband`s education, place of residence, husband`s occupation, respondent`s working status and region have highly significant impact on age at first marriage. Poisson regression analysis shows that completed fertility significantly varies between two cohorts in different divisions. Muslim women have more children compared to other religions. Women living in urban area, educated and employed women, tend to have lower completed fertility.Keyword: Age at marriage, completed fertility, poisson regression, cohort analysis, media exposed
      PubDate: 2014-12-22
      Issue No: Vol. 3 (2014)
  • Study of Generalised Class of Estimator in Presence of Non Response
    • Authors: B.K. Singh, Yater Tato
      Abstract: In this paper, we have suggested a generalised class of dual to ratio estimator of the population mean of the variable of interest y in the presence of non-response in two situations. The expressions for bias and mean square error have been obtained and their properties are studied. An empirical study is carried out to support the theoretical results.Keywords: Dual to ratio, bias, mean square error (MSE), non response, efficiency
      PubDate: 2014-12-15
      Issue No: Vol. 3 (2014)
  • Distribution Free Test for Scale Parameter under Standard Logistic
    • Authors: Md. Siddikur Rahman, Zahir Iqbal, Swapan Kumar Dhar
      Abstract: This paper proposes a distribution free test for testing the scale parameters of standard logistic distribution. The suitability of the proposed test in this paper has been investigated by Monte Carlo simulation and all the result in this paper are for two sample case problem. Powers of the proposed test are compared with different existing test. The proposed test performs better than other existing tests.Keywords: Logistic distribution, distribution free test statistic, scale parameter, Monte Carlo simulation
      PubDate: 2014-12-15
      Issue No: Vol. 3 (2014)
  • Construction of Neighbour Balanced Nested Row Column Designs and
           μ-Resolvable All Order Neighbour Balance Design by using Mutually
           Orthogonal Latin Squares
    • Authors: Aatish Kumar Sahu, Anurup Majumder
      Abstract: Latin Squares are known to possess very unique features and so is its utility. Construction of Balance Incomplete Block with nested Row Column (BIBRC) designs having Neighbor Balanced properties have been developed on the concept of Mutually Orthogonal Latin Squares (MOLS) of strength v, v being natural number and if it has at least four MOLS available. The designs used minimal blocks and found to be exact neighbor balanced with respect to rows, columns as well as diagonally. In the second part of this paper, concept of MOLS is used in construction of µ-Resolvable Balance Incomplete Block Designs following Subramani [31]. The designs fulfill the criteria of one-dimensional All Order Neighbor Balanced (AONB), developed with v number of treatments, v being natural number, if and only if, there is availability of minimum two Mutually Orthogonal Latin Squares for v. These designs showed all order neighbor balanced with minimal number of blocks at v(v-1)/2.
      PubDate: 2014-09-22
      Issue No: Vol. 3 (2014)
  • A Generalized Product Method of Estimation in Two Phase Sampling
    • Authors: Balkishan Sharma, Houshila P. Singh, Rajesh Tailor
      Abstract: This paper proposes a generalized product type estimator for population mean using two phase sampling in the presence of available knowledge on second auxiliary variable z, when the population mean of the main auxiliary variable x is not known. It is shown that the proposed estimator is more efficient than the usual unbiased estimator, the double sampling product estimator and Sahoo et al.’s estimator. An empirical study is carried out to assess the comparative performance of the proposed estimator over other estimators.
      Keywords: Study variate, Auxiliary variate, Bias, Mean squared error, Double sampling
      PubDate: 2014-09-18
      Issue No: Vol. 3 (2014)
  • Mann-Whitney Test for Imprecise Observations
    • Authors: V. S. Vaidyanathan
      Abstract: Mann-Whitney test is a non-parametric test that is used to identify whether the probability distributions corresponding to two populations are identical. This article extends the Mann-Whitney test by treating the underlying observations as imprecise values. The test procedure is developed by using a novel approach to rank fuzzy values based on the concepts of “Credibility Theory” proposed by Liu (2007) for studying the behavior of fuzzy phenomena. Numerical illustration is provided through simulation by representing the observations as triangular fuzzy numbers.
      Keywords: Credibility measure, Fuzzy number, Membership function, Ranking fuzzy values, Mann-Whitney test statistic
      PubDate: 2014-09-18
      Issue No: Vol. 3 (2014)
  • Coefficient Estimation of Regression Model and Hypothesis Testing by
           Bootstrap Method
    • Authors: Md. Siddikur Rahman
      Abstract: The main concern of statistical inference is to achieve accurate result and to make proper decision on the basis of sample observations. But in some practical cases, it is not possible to reach the goal of statistics for the lack of desired number of sample. When the sample size is small and/or the empirical distribution is unknown, we have to use bootstrapping method to increases the accuracy of the results. The bootstrap method of regression analysis is discussed in this paper with practical example. In small sample case, there is a possibility of violating the normality assumption of the error. To avoid this problem, the bootstrap method gives us better result. A key objective in classical testing of statistical hypothesis is achieving good power of the test. To compare the existing simulation based test approach to bootstrap approach test, we calculated the power of the test and then graphically shown in this paper. We have conducted a hypothesis testing of regression coefficient. We observe that power of the test with bootstrap approach is much higher than the power of simulation approach. Actually, the power of the tests is compared and the better result of bootstrap method is found.
      Keywords: Linear Regression model, Regression coefficient, Hypothesis testing, Bootstrapping
      PubDate: 2014-08-21
      Issue No: Vol. 3 (2014)
  • A New Form of Sam-Solai’s Multivariate Generalized Normal
    • Authors: David Sam Jayakumar, A. Solairaju, A. Sulthan
      Abstract: This paper proposed a new generalization of family of Sarmanov type Continuous multivariate symmetric probability distribution with reference to a new form of Sam-Solai’s Multivariate Generalized normal distribution from univariate case. Further, we find its Marginal, Conditional distributions, Generating functions and also discussed it’s special cases.The shape parameter played a significance role and it determines the family of some existing multivariate distributions as subclass of the proposed multivariate generalized normal distribution. The special cases include the transformation of MVGND into Generalized log-normal distribution and Sam-Solai’s Multivariate log-Laplace distribution. The following results are redundant: (1)Sam-Solai’s Multivariate Laplace distribution, (2) Sam-Solai’s Multivariate Gaussian normal distribution, (3)Sam-Solai’s Multivariate mixture of normal-Laplace distribution, (4) Sam-Solai’s Multivariate and (5) Sam-Solai’s Multivariate log-normal distribution. Moreover, it is found that the conditional variance of Sam-Solai’s Multivariate generalized conditional normal distribution is heteroskedastic and the correlation co-efficient between any two generalized normal random variables determined by the shape parameters .Finally, area values of the Bivariate Generalized normal distribution are extracted and bivariate probability surfaces are visualized for different values of shape parameters.

      Keywords: Sarmanov type, Sam-Solai’s Multivariate Generalized normal distribution, Conditional variance, Heteroskedastic, shape parameter
      PubDate: 2014-05-07
      Issue No: Vol. 3 (2014)
  • Individual Patient Data Meta-Analysis using Proportional Hazard Models
    • Authors: Md. Nuruzzaman Forhad, Md. Erfanul Hoque, Md. Belal Hossain
      Abstract: One alternative to classical meta-analytic approaches is known as individual patient data (IPD) meta-analysis. Rather than depending on summary statistics calculated for individual studies, IPD meta-analysis analyzes the complete data from all included studies. The IPD meta-analysis is considered the gold-standard for synthesizing survival data. In this paper, an attempt has been made to introduce the use of parametric and semi-parametric proportional hazard models to perform one and two-step IPD meta-analysis of time-to-event outcomes. Three parametric PH models: exponential PH model, Weibull PH model, log-logistic PH model and one semi-parametric PH model: Cox PH model have been used for this purpose. The parameter estimation procedure has been illustrated in two-step approach and finally hazard ratio has been calculated. For the illustration of the proposed framework, the demographic health survey (DHS) data for ten countries has been used. An investigation is made to assess the impact of place of residence on child mortality by applying our proposed IPD meta-analysis methods and finally make a comparison of the rate of child mortality between rural and urban area. Here different studies (different countries) show contradictory results but after performing proposed meta-analysis approach the actual impact of place of resident on child mortality has been found. The given approach provides an appropriate guideline to get the better estimated values by using the appropriate model to the data. If the distribution of the data is known then one can easily gets the appropriate result using this approach.
      Keywords: Hazard ratio, Individual patient data, Proportional hazard model, Meta-analysis
      PubDate: 2014-05-07
      Issue No: Vol. 3 (2014)
  • Hybrid Poisson Distribution
    • Authors: Sampath Sundaram, Deepa S P
      Abstract: In this paper, hybrid version of Poisson distribution using the Chance Theory due to Liu (2008) is developed. The process of computing chance values of various events, mean and variance of hybrid poisson distribution using an evolutionary algorithm, namely, genetic algorithm are discussed with some illustrative examples.
      Keywords: Hybrid variable, Chance distribution, Hybrid binomial distribution, Hybrid poisson distribution
      PubDate: 2014-05-07
      Issue No: Vol. 3 (2014)
    • Authors: Narendra Singh Thakur
      Abstract: In this paper we present some imputation methods to estimate the population mean in presence of missing data under stratified sampling design. The suggested methods are discussed in simple random sampling as well. The expression of bias and MSE are derived in the form of population parameters using the concept of large sample approximation upto first order. A Comparative study is considered between stratified and simple random sampling. The empirical study is carried out over two real populations.
      PubDate: 2014-05-07
      Issue No: Vol. 3 (2014)
  • Measures of Location for Imprecise Data
    • Authors: V. S. Vaidyanathan
      Abstract: Statistical analysis is usually done on data sets that contain precise information. However, data obtained may not be precise always. This may be due to vagueness in the process of measurement itself or due to the values being expressed in linguistic terms. Data that are not precise are referred to as imprecise data or fuzzy data. Developing statistical measures for imprecise data has been pursued by researchers during the past decade. However, the methodologies adopted involve operations on fuzzy numbers through α-cut approach, thereby making the process difficult. Liu (2007) developed a mathematical theory for studying the behavior of fuzzy phenomena known as “Credibility Theory”. This theory provides operations on fuzzy numbers that do not depend on the α-cut approach. In this paper, a methodology for obtaining measures of location for imprecise data is developed by using the concepts available in “Credibility Theory”. Numerical Illustration for calculating the proposed measures is also provided.   
      PubDate: 2014-01-16
      Issue No: Vol. 3 (2014)
  • Modified Joint Test of Heteroscedasticity and Serial Correlation in a
           Random Effect Panel Data Model under Restricted Alternatives
    • Authors: Nahid Salma, Ajit Kumar Majumder
      Abstract: In time series econometric theory, the sign of the parameter may be pre-assigned, that is the parameter may be ordered or restricted. Estimation of this restricted parameter is then a vital problem. If we know the parameters are restricted by some constraints, it is reasonable to expect that we should be able to do better by incorporating such additional information than by ignoring them. The paper concerned with estimating and testing restricted hypotheses in Panel data regression model. The aim of the paper: constructing a modified LM test statistic to test the joint effect of heteroscedasticity and serial correlation in a random effect error component model, where the hypotheses are restricted. Monte Carlo results show that the tests have good size and power under various forms of heteroscedasticity and serial correlation. 
      PubDate: 2014-01-16
      Issue No: Vol. 3 (2014)
  • Construction of Neighbour Balanced BIBRC Designs
    • Authors: Aatish Kumar Sahu, Anurup Majumder
      Abstract: Construction of a series of Balance Incomplete Block with nested Rows and Columns (BIBRC) designs having Neighbor Balanced properties has been presented in this paper. The series of BIBRC designs has been developed on the concept of mutually orthogonal mates (MOM’s) of existing BIBRC designs with v as a prime number. The designs thus constructed are found to be first order neighbor balanced with respect to rows, columns as well as diagonally, with every pair of treatment occurred in immediate neighboring plots nr times in rows, nc times in columns and nd times in diagonals respectively.  
      PubDate: 2014-01-15
      Issue No: Vol. 3 (2014)
  • Heteroscedasticity in Survey Data and Model Selection Based on Weighted
           Schwarz-Bayesian Information Criterion
    • Authors: G. S. David Sam Jayakumar, Sulthan A
      Abstract: This paper proposed Weighted Schwarz Bayesian Information criterion for the purpose of selecting a best model from various competing models, when heteroscedasticity is present in the survey data. The authors found that the information loss between the true model and fitted models are equally weighted, instead of giving unequal weights. The computation of weights purely depends on the differential entropy of each sample observation and traditional Schwarz Bayesian information criterion was penalized by the weight function which comprised of the Inverse variance to mean ratio (VMR) of the fitted log-quantiles. The weighted Schwarz Bayesian information criterion was proposed in two versions based on the nature of the estimated error variances of the model namely Homogeneous and Heterogeneous WSBIC, respectively. The proposed WSBIC is different from the traditional information criterion of model selection and it leads to conduct a logical statistical treatment for selecting a best model. Finally this procedure was numerically illustrated by fitting 12 different types of stepwise regression models based on 44 independent variables in a BSQ (Bank service Quality) study.  
      PubDate: 2014-01-15
      Issue No: Vol. 3 (2014)
  • Maternal Health Care Utilization of Married Young Women in Bangladesh
    • Authors: Rebeka Sultana, Sabina Islam, Abdul Baten
      Abstract: The study attempts to investigate the health care utilization among married young women during childbirth and postpartum in Bangladesh. The nationwide data of Bangladesh Demographic and Health Survey-2007 is used to focus on births that occurred in the five years preceding the survey period. The study revealed that during childbirth about 19 percent of respondent received assistance and above 21 percent of mother received postnatal Care (PNC) from medically trained health provider. It is found that about 16 percent of respondent have taken place their delivery at health facility during last live birth. The study adopted various statistical techniques viz., univariate, bivariate and logistic regression analysis. In Bivariate analysis, it was found that almost all the selected socio-cultural, program related and demographic variables have significant association with maternal health care utilization except the characteristic age difference between spouses. Logistic regression analysis revealed that education and wealth index are positively related with delivery care and PNC of young married women around the time of birth. The study suggests it is important that programs aimed at improving maternal health include targeting young women, especially those from rural areas with low levels of education and from poor household, given their high risk around the time of birth. 
      PubDate: 2014-01-15
      Issue No: Vol. 3 (2014)
  • Seasonal ARIMA for Forecasting Sea Surface Temperature of the North Zone
           of the Bay of Bengal
    • Authors: Md. Rezaul Karim
      Abstract: The behavior of the sea surface temperature (SST) of the north zone of the Bay of Bengal plays an important role for understanding climate changes over Bangladesh. The monthly average of SST of this zone is used in this study which is obtained from January 1900 to December 2009. Box and Jenkins method is used to fit a seasonal autoregressive integrated moving average (ARIMA) model used in forecasting SST of the north zone of the Bay of Bengal. The most commonly used model selection criteria’s such as the Akaike’s information criterion (AIC), the Bayesian information criterion (BIC), etc. are used for model comparison. The Root Mean Squared Error, Mean Absolute Error and Mean Absolute Percent Error are also used for diagnostic checking in model selection procedure. Seasonal ARIMA (2, 0, 1) (0, 1, 1)12 model is suggested for forecasting the SST of the north zone of the Bay of Bengal.
      PubDate: 2013-09-17
      Issue No: Vol. 3 (2013)
  • Estimation and Projection of Urban Population of India and China
    • Authors: M. N. Megeri, Kengnal Prakash
      Abstract: The world urban population is expected to be double by 2050, increasing from 3.6 billion in 2011 to 6.3 billion in 2050 (UN, 2011). The urban population of India and China increasing exponentially over period of time the growth of urban population of India is slower than China after 1981 census. The urban population is projected with the help of past data. There are two types of approaches for calculating projections, viz macro and micro approach (Goldstain and Arriaga, 1975). The data collected for this study is from various censuses for India and data for China is collected from website The urban population of India and China is projected from 1991–2051 by using Ratio Method, URGD Method and Logistic Growth Curve Method. The analysis of the study reveals that the projected urban population of India is over estimated by Ratio Method and under estimated by URGD Method and logistic Growth Curve Method. In case of China projected urban population is under estimated for all the methods. And also shows that the URGD Method for China and Logistic Growth Curve Method for India gives reasonable projected of urban population. 
      PubDate: 2013-09-17
      Issue No: Vol. 3 (2013)
  • Bayesian Approach for Gender Differentiation by Finger Ridges Count
    • Authors: Hom Nath Dhungana, Kamal kishore Sahu
      Abstract: Classification of gender from fingerprints is an important step in forensic anthropology in order to identify the gender of a person. Fingerprints are considered to be the most reliable criteria for personal identification. The present analysis was undertaken to observe the distribution of finger print pattern in males and females from U.P. The objective of the present study was to study the differences in the finger loop ridge count among males and female subjects. Statistical analysis revealed significant mean difference in the finger loop ridge counts between genders.  
      PubDate: 2013-09-17
      Issue No: Vol. 3 (2013)
  • An exact Kolmogorov–Smirnov Test for the Logarithmic Series
           Distribution with Unknown Parameter
    • Authors: Arnab Hazra
      Abstract: In this paper, we develop an exact Kolmogorov–Smirnov goodness-of-fit test in the case of logarithmic series distribution with an unknown parameter value. This test is conditional, with the test statistic being the maximum absolute difference between the empirical distribution function and its conditional expectation given the sample total. Some modifications are done on an algorithm previously proposed in the case of the Poisson distribution and used the modified algorithm for obtaining the exact critical values. We illustrate the test with three examples. We also include some simulations in order to investigate the power of the procedures. The new test seems to be the first exact goodness-of-fit test for logarithmic series distribution for which critical values are available without simulation or exhaustive enumeration.

      PubDate: 2013-09-17
      Issue No: Vol. 3 (2013)
  • Job Sequencing with Fuzzy Processing Times using Credibility Theory
    • Authors: V. S. Vaidyanathan
      Abstract: In this paper, a new algorithm to find an optimal sequence of ‘ ’ jobs that has to be processed through ‘ ’ machines is developed by treating the processing times of jobs on the machines as fuzzy (imprecise) variables. The algorithm is similar to that of Johnson (1954) which considers the processing times as precise in nature. The proposed algorithm makes use of the concepts of ‘Credibility Theory’ due to Liu (2008). An illustration of the proposed algorithm is given by representing the processing times as triangular fuzzy numbers. 
      PubDate: 2013-05-11
      Issue No: Vol. 3 (2013)
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