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Journal of the Indian Society for Probability and Statistics
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ISSN (Online) 2364-9569
Published by Springer Publishing Company

[24 journals]

On First Order Autoregressive Asymmetric Logistic Process
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  Abstract: Abstract An additive first order autoregressive model with logistic distribution as marginal is studied. We have obtained a representation of the innovation random variable using stable random variable. In order to model asymmetric data, we have introduced asymmetric logistic distribution and first-order autoregressive asymmetric logistic process. We discussed some important properties of the processes. Model parameters are estimated by least square and Gaussian methods. We conducted a simulation study for checking the accuracy of the parameter estimation methods. As an application, we modelled population growth time series data using the proposed models.
  PubDate: 2023-02-03
Exponential Intervened Poisson Distribution: Characterizations, Different
Methods of Estimation and Applications
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  Abstract: Abstract In this paper, four characterizations of exponential intervened Poisson (EIP) distribution are obtained. The characterizations are based on hazard function, reversed hazard function and conditional expectation. Estimation of the parameters of EIP distribution is performed through maximum likelihood, ordinary least squares, weighted least squares and Cramer-von Mises methods of estimation. A simulation study is carried out to assess the performance of the four estimation methods in mean square error sense. A real data application is also carried out for the comparison of the estimation methods and to show the potentiality of the EIP model.
  PubDate: 2023-01-09
Bayesian Linear Restricted Least Squares Estimators
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  Abstract: Abstract Bayesian Statistics had been outshined classical Statistics over the years due to its probabilistic approach to modelling and data analytics. In recent times, much of model complexity and data ambiguity emerged of which the existing methods have their drawbacks. Model complexity and data uncertainty most times exhibit multicollinearity which render the inferences of least squares invalid. This then call for improvement in the existing methods so as to capture the trend in model complexity and data uncertainty. The Monte Carlo simulations was adopted to compare the restricted least squares family of estimators (RLSFE) with the presence of multicollinearity and two sets of linear restrictions were imposed on the model. The risk values and relative efficiency of the RLSFE under quadratic loss function were estimated to compare the estimators. Bayesian restricted least squares estimator was derived, the posterior mean and Bayes estimate were deprioritised with prior mean. The study found out that posterior mean and Bayes estimates outperformed classical restricted least squares estimators due to their lower risk values. The relative efficiency pointed to the fact that posterior mean and Bayes estimates are most preferred and efficient. The study further observed monotonic increase in the risk values as the $\rho$ increases which proved the negative impact of multicollinearity of the inferences of regression parameters.
  PubDate: 2022-12-12
Preliminary Test Regression Estimator in Double Sampling Based on
Two-Stage and Ranked Set Sampling with Two Auxiliary Variables
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  Abstract: Abstract In this paper a preliminary test regression estimator for estimating the population mean of study variable Y is suggested for the two-stage sampling using ranked set sampling in the second stage when there is partial information on both of the two auxiliary variables X and Z. The variables (X, Y, Z) are considered to follow a trivariate normal distribution. Bias and mean square error of the proposed estimator are computed and comparison is made with the usual regression estimator under the same sampling scheme with two auxiliary variables analytically and numerically.
  PubDate: 2022-11-28
Normal-Power-Logistic Distribution: Properties and Application in
Generalized Linear Model
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  Abstract: Abstract The applications of Normal distribution in literature are verse, the new modified univariate normal power distribution is a new distribution which is adequate for modelling bimodal data. There are many data that would have been modelled by normal distribution, but because of their bimodality, they are not, since normal distribution is unimodal. In this paper, a new extension of the normal linear model called the normal-Power generalized linear model, derived from the T-Power $\lbrace$ Logistic $\rbrace$ framework is presented. The statistical properties of the distribution and the proposed model were derived such as quantiles, median, mode, robust skewness, robust kurtosis and moment. The maximum likelihood estimation method was considered to obtain the unknown model parameters. Three real data sets were analyzed to demonstrate the flexibility and usefulness of the proposed model. The new model would be very useful as alternative in cases where skewed or bimodal response variables, which are not well fitted with normal linear model.
  PubDate: 2022-11-19
On Estimation of Type-II Progressive Censored Erlang Distribution
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  Abstract: Abstract Progressive censoring has become popular in recent years. In this paper, Type-II progressive censored Erlang distribution has been used for Bayesian estimation and maximum likelihood estimation. Method of elicitation has also been employed by using prior predictive distributions to compute the values of hyperparameters. Moreover, real-life data and rigorous simulation schemes have been exercised for Bayesian shrinkage estimates, Bayesian estimates, and maximum likelihood estimates along with their associated posterior risks. Furthermore, the results of Bayes estimates are obtained by using a generalized entropy loss function. During this meticulous exercise, it has been observed that by increasing the effective sample size $n$ , risks become decrease and the Bayes estimates turn out to be closer to the true value of the parameters. But at the same time, both Bayes estimates and risks are not affected by changing the sample size $m$ . Additionally, Bayesian shrinkage estimation is more tractable than Bayesian estimation and maximum likelihood estimation especially when prior information about the parameter is known in the form of point guess value.
  PubDate: 2022-09-29
Construction of an Alternative Bivariate Distribution with Discrete
Modified Weibull as Marginals
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  Abstract: Abstract An alternative version of bivariate discrete Weibull distribution with marginal densities as discrete modified Weibull distribution is constructed. Certain important properties of the model viz. joint distribution function, joint probability mass function, marginal distributions, moment generating function and conditional distributions are derived so as to enable this model in the practical application of reliability analysis such as risk modelling and shock modelling. The parameters of the model are estimated through method of maximum likelihood estimation and compared the performance of our model with other existing bivariate models. The usefulness of the model is illustrated through some real life data sets. A simulation study is carried out using Monte Carlo simulation and computed the bias of various estimators of our model.
  PubDate: 2022-09-22
On the Test of Association Between Nonparametric Covariate and Error in
Semiparametric Regression Model
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  Abstract: Abstract Consider a semiparametric regression model $Y=Z\beta +m(X)+\epsilon$ , with Y being the response variable, X and Z being the covariates, $\beta$ the unknown parameter, $m(\cdot )$ an unknown function preferably a non-linear one, and $\epsilon$ the random error. In this article, our objective is to test the independence between X and $\epsilon$ only, given the assumption of no relationship between Z and $\epsilon$ . Using the concept of Robinson’s (Econometrica 56:931–954, 1988) technique of $\beta$ estimation at the first stage and then considering a transformed nonparametric model, test statistic is formed on the function of induced order statistics of Y. Thereafter constructing Le Cam’s contiguous alternatives, the local powers of the proposed rank-based test statistic as well as power performances of some other relevant statistics are discussed. Further, in reference to the finite sample simulation study, the power performance of newly introduced test is investigated. Finally, for a real biological data the practicability of the proposed test technique under the setting of semiparametric regression model is judged.
  PubDate: 2022-09-15
Intuitive Derivation of Some Tests for Right Censored Data
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  Abstract: Abstract Two sample tests for right censored survival data require complicated assumptions that are sometimes not satisfied in practice. The estimated treatment effect is difficult to understand. Some papers that advocate for using the difference in restricted mean survival time, the difference in the estimated survival curves at a fixed time point, or the average difference over a pre-determined time interval, among others. The rationale for these alternative methods is that they are easier to interpret and do not require the proportional hazards assumption. The purpose of this paper is to provide some intuition for some of these tests.
  PubDate: 2022-08-17
Analysis of Reliability of Interdependent Serial, Parallel and The General
$$ k\hbox {-}out\hbox {-}of\hbox {-}n: G $$ k - o u t - o f - n : G
System: A New Approach
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  Abstract: Abstract Interdependence between random variables and processes is analyzed extensively in the literature using different techniques. In this paper, a new direction of analysis to investigate the reliability of systems such as a $ k\hbox {-}out\hbox {-}of\hbox {-}n: G $ system and, in particular serial and parallel systems with interdependence among the components, is introduced. This procedure is through a special case of semi-Markov process. The distribution of the time to failure of serial, parallel and also that of the more general $ k\hbox {-}out\hbox {-}of\hbox {-}n: G $ system, are derived. A theoretical comparison between systems with interdependent components and systems with independent components is provided.
  PubDate: 2022-07-22
On the Generalized Sibuya Distribution
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  Abstract: Abstract In this paper, we derive hitherto unknown expressions for the generalized Sibuya distribution Kozubowski and Podgórski (Ann Inst Stat Math 70(4):855–887, 2018), which include shape properties, order statistic properties, distribution of sample range, conditional distributions of extreme order statistics, stress strength probability, sum of random variables, Shannon entropy, maximum likelihood estimation and censored maximum likelihood estimation. Finally, two data illustrations are provided.
  PubDate: 2022-07-14
A Note on Asymptotic Distribution of Trimmed Mean
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  Abstract: Abstract This article investigates the behavior of the asymptotic distribution of the trimmed mean when the data follow normal, Laplace and Cauchy distributions. This detailed analytical characterization is done for the aforementioned cases.
  PubDate: 2022-07-11
Extended Farlie-Gumbel-Morgenstern Bivariate Bilal Distribution
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  Abstract: Abstract The extended Farlie-Gumbel-Morgenstern bivariate Bilal distribution (EFGMBBD) is a new bivariate Bilal distribution (BD) introduced in this paper, as well as the distribution theory of concomitants of order statistics (COS) that results from it. We used the ranked set sampling (RSS) technique proposed by Stokes (1977) to estimate the parameter associated with the distribution of the study variable Z of primary interest when (W, Z) follows an EFGMBBD. We have developed two estimators, an unbiased estimator based on Stoke’s RSS and the best linear unbiased estimator (BLUE) based on Stoke’s RSS when the dependence parameter related to Z is known. This paper also compares the efficiency of the unbiased estimator and the BLUE concerning the asymptotic variance of the maximum likelihood estimator (MLE).
  PubDate: 2022-06-30
Use of Concomitants of Order Statistics in the Estimation of Parameters
$$\mu _2$$ μ 2 and $$\sigma _2$$ σ 2 of Morgenstern Type Bivariate
Exponential Distribution
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  Abstract: Abstract In this article we have derived the best linear unbiased estimator (BLUE)of the parameters $\mu _1$ , $\mu _{2}$ , $\sigma _1$ and $\sigma _{2}$ involved in the Morgenstern type bivariate exponential distribution(MTBED) by concomitants of order statistics .Also we have evaluated coefficients of the BLUE’s of $\mu _1$ , $\mu _{2}$ , $\sigma _1$ and $\sigma _{2}$ involved in the Morgenstern type bivariate exponential distribution by concomitants of order statistics for some specific values of the sample size m .Also we have derived the asymptotic variances of the MLE’s of the parameters $\mu _1$ , $\mu _2$ , $\sigma _1$ and $\sigma _2$ involved in MTBED.A simulation study is also conducted for estimating the parameters involved in MTBED.
  PubDate: 2022-06-29
A Nonparametric Two-Sample Test for Scale Using Linear Combination of
Quadratic and Linear Function of Placements
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  Abstract: Abstract We propose a distribution-free test for the nonparametric two-sample scale problem. We discuss the problem of testing the homogeneity of two populations against scale alternatives. Contrary to the usual assumption that both populations have a common median, we assume both populations to have a common quantile of order α; not necessarily half. Without loss of generality, the common quantile is assumed to be equal to zero. This statistics uses the concept of placement of observations from a population having more spread around common quantile as compared to the observations from the other population. The construction of the statistics is similar to the construction of statistics proposed by Sukhatme (Ann Math Stat 28:188–194, 1957) and Deshpande and Kusum (Austrl J Stat 26:16–24, 1984). It shows that the new test is more efficient than the Sukhatme, Deshpande-Kusum, and Mood Test (Mood in Ann Math Stat 34:973–983, 1954) in Pitmen ARE. We further show through Monte Carlo simulation that the Test has good power when the common quantile is in the tails of the distribution than Sukhatme Test and Deshpande-Kusum test.
  PubDate: 2022-06-20
An Improved Two-Stage Forced Randomized Response Model for Estimating the
Proportion of Sensitive Attribute
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  Abstract: Abstract Randomized response technique is a useful method in surveys for extracting answers to sensitive questions, using a randomization device. In this paper, a two-stage forced answer randomised response model for estimating a sensitive attribute has been proposed. The proposed strategy is found to be more simple and efficient than existing RRT models for estimating the sensitive attribute, under certain practical situations. Privacy of the respondents possessing the sensitive attribute is also well protected in the proposed procedure. The superiority of the proposed model has been established with the help of a simulation study.
  PubDate: 2022-06-17
On Bivariate Dynamic Survival Extropy and Its Estimation
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  Abstract: Abstract Recently (Lad and Sanfilippo 2015) proposed extropy as a complement dual of Shannon’s entropy in the univariate case. This paper extended the concept of extropy to the conditional and bivariate cases and studied its essential properties. An empirical and kernel estimators for the proposed measure have been introduced. To study the performance of the estimators, we carried out simulation and real data analysis.
  PubDate: 2022-06-17
An Overview of Univariate and Multivariate Karhunen Loève Expansions
in Statistics
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  Abstract: Abstract Dependent data are ubiquitous in statistics and across various subject matter domains, with dependencies across space, time, and variables. Basis expansions have proven quite effective in modeling such processes, particularly in the context of functional data and high-dimensional spatial, temporal, and spatio-temporal data. One of the most useful basis function representations is given by the Karhunen-Loève expansion (KLE), which is derived from the covariance kernel that controls the dependence of a random process, and can be expressed in terms of reproducing kernel Hilbert spaces. The KLE has been used in a wide variety of disciplines to solve many different types of problems, including dimension reduction, covariance estimation, and optimal spatial regionalization. Despite its utility in the univariate context, the multivariate KLE has been used much less frequently in statistics. This manuscript provides an overview of the KLE, with the goal of illustrating the utility of the univariate KLE and bringing the multivariate version to the attention of a wider audience of statisticians and data scientists. After deriving the KLE from a univariate perspective, we derive the multivariate version and illustrate the implementation of both via simulation and data examples.
  PubDate: 2022-06-09
Unit Exponentiated Fréchet Distribution: Actuarial Measures, Quantile
Regression and Applications
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  Abstract: Abstract In this study, a new distribution is developed for modelling responses on the unit interval. Several properties including moments, order statistics and stochastic ordering of the distribution are derived. Also, several actuarial measures, including risk measures and premium principles, are derived and Monte Carlo simulation studies performed on them. Different parameter estimation methods are used to estimate the parameters of the distribution. The performances of the estimators are assessed via Monte Carlo simulation studies. A quantile regression model is developed based on the distribution. Two different applications are carried out to assess the performance and usefulness of the distribution on both univariate data and data with covariates. The performance of both the distribution and its quantile regression model indicates that the new distribution can serve as an alternative to modelling actuarial data on unit interval.
  PubDate: 2022-06-07
On the Asymptotic Behaviour of Extremes of Observations from a Tempered
Stable Distribution
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  Abstract: Abstract In this article, we obtain the limit distribution of the maxima and minima of independent observations from tempered stable and bilateral gamma distributions, and provide simple closed form expressions for the associated norming constants. We explore the associated near-maxima and near-minima random variables. We also discuss some applications.
  PubDate: 2022-06-01