Journal of the Iranian Statistical Society
https://jirss.irstat.ir/
Journal of the Iranian Statistical Societyendaily1Wed, 01 Jun 2022 00:00:00 +0430Wed, 01 Jun 2022 00:00:00 +0430Nonparametric Estimation of the Residual Entropy Function with Length-Biased Data
https://jirss.irstat.ir/article_703882.html
We propose a nonparametric estimator for the residual entropy function based on length-biased data. Some asymptotic results have been proved. The strong consistency and asymptotic normality of the proposed estimator are established under suitable regularity conditions. Monte Carlo simulation studies are carried out to evaluate the performance of the estimator using the bias and mean-squared error. A real data set is considered, and we show that the data follow a length-biased distribution. Moreover, the proposed estimator yields a better value for the estimated residual entropy in comparison to the competitor estimator.Modeling Chile Fishing Data Using Environmental Exogenous Variables with GARCH-X Model
https://jirss.irstat.ir/article_704625.html
Fishing industry has always been an economic motor in many countries around the world, but the fisheries production faces a lot of uncertainty and instability due to the complex factors involved in its operations. In this article, we consider the problem of modeling Chile fishing data using environmental exogenous variables with generalized autoregressive conditional heteroskedasticity (GARCH-X) type models. We carried out this by proposing an ARMA type model for the mean with GARCH-X noise. First, the ARMA, GARCH and GARCH-X models are briefly introduced and the data is described. The exogenous variables are selected from a group of environmental and climatic indicators by correlational analysis. Then, ARMA GARCH and ARMA GARCH-X models with exogenous variables are fitted and compared by information criteria and classical error measures, and stability of its parameters are checked. The statistical tests and comparisons evidenced that a model with inclusion of external variables in mean and variance with the ARMA GARCH-X specification performed better and adjusted the observed values more rigorously. Finally, some conclusions and possible refinations of the applied techniques are given.Two-Step Calibration Estimator with Double Use of Auxiliary Variable: Method and Application
https://jirss.irstat.ir/article_704624.html
This article introduces a two-step calibration technique for the inverse relationship between study variable and auxiliary variable along with the double use of the auxiliary variable. In the first step, the calibration weights and design weights are set proportional to each other for a given sample. While in the second step, the constant of proportionality is to be obtained on the basis of some different objectives of the investigation viz. bias reduction or minimum Mean Squared Error (MSE) of the proposed estimator. Many estimators based on inverse relationship between $x$ and $y$ have been already developed and are considered to be special cases of the proposed estimator. Properties of the proposed estimator is discussed in details. Moreover, a simulation study has also been conducted to compare the performance of the proposed estimator under Simple Random Sampling Without Replacement (SRSWOR) and Lahiri-Midzuno (L-M) sampling design in terms of percent relative bias and MSE. The benefits of two-step calibration estimator are also demonstrated using real life data.Quantile based Past Geometric Vitality Function of Order Statistics
https://jirss.irstat.ir/article_704623.html
Nair and Rajesh (2000)&nbsp;introduced the geometric vitality function, which explains the failure pattern of components or systems based on the component's geometric mean of the remaining lifetime. Recently quantile-based studies have found greater interest among researchers as an alternative method of measuring the uncertainty of a random variable. The quantile-based measures possess some unique properties to the distribution function approach. The present paper introduces a quantile-based past geometric vitality function of order statistics and its properties. Finally, we provide an application for the new measure based on some distributions which are useful in lifetime data analysis.Transformer Self-Attention Network for Forecasting Mortality Rates
https://jirss.irstat.ir/article_704621.html
The transformer network is a deep learning architecture that uses self-attention mechanisms tocapture the long-term dependencies of a sequential data. The Poisson-Lee-Carter model, introduced to predict mortality rate, includes the factors of age and the calendar year, which is a time-dependent component. In this paper, we use the transformer to predict the time-dependent component in the Poisson-Lee-Carter model. We use the real mortality data set of some countries to compare the mortality rate prediction performance of the transformer with that of the long short-term memory (LSTM) neural network, the classic ARIMA time series model and simple exponential smoothing method. The results show that the transformer dominates or is comparable to the LSTM, ARIMA and simple exponential smoothing method.Corrected Likelihood Estimation in Semiparametric Linear Mixed Measurement Error Models: Asymptotic Results
https://jirss.irstat.ir/article_704615.html
This paper is concerned with the estimation problem in semiparametric linear mixed models when some of the covariates are measured with errors. The authors proposed the corrected score function estimators for the parametric and non parametric components. The resulting estimators are shown to be consistent and asymptotically normal. An iterative algorithm is proposed for estimating the parameters. Asymptotic normality of the estimators is also derived. Finite sample performance of the proposed estimators is assessed by Monte Carlo simulation studies. We further illustrate the proposed procedures by an application.Analysis of Dependent Competing Risk Model in the Presence of Joint Type-II Censoring Using Bivariate Marshll-Olkin Family
https://jirss.irstat.ir/article_704614.html
Lifetime data has several applications in different fields such as Biology and Engineering. Failures for this type of data may occur due to several causes. In real world, causes of failures are interacting together which violates the independency assumption. Once dependency between failures is satisfied, bivariate families should be used to analyze the data. In literature, the majority of studies handle the case when data come from one source. However, in real life, data could come from different sources. One way to analyze data from different sources together and reduce the time and cost of the experiment is joint type-II censoring. To the best of our knowledge, joint type-II censoring was not yet derived using bivariate lifetime distributions. In this paper, we derive the likelihood function of joint type-II censoring using bivariate family in the presence of dependent competing risks. A simulation study is performed and two real datasets are analyzed.Estimation for the Three-Parameter Exponentiated Weibull Distribution under Progressive Censored Dat
https://jirss.irstat.ir/article_704612.html
In this paper, we consider the problem of estimating the unknown parameters of an exponentiated Weibull distribution when the data are observed in the presence of progressively Type II censoring. We observed that the maximum likelihood estimators do not have a closed form, and so require a numerical technique to compute, further the implementation of the EM algorithm still requires the numerical techniques. So we employ the stochastic expectation-maximization (SEM) algorithm to estimate the model parameters and further to construct the associated asymptotic confidence intervals of the unknown parameters. Moreover, under Bayesian approach, we consider symmetric and asymmetric loss functions and compute the Bayesian estimates using the Lindley&rsquo;s approximation and Gibbs sampler together with Metropolis Hastings algorithm. The highest posterior density (HPD) credible intervals are also constructed. The behavior of suggested estimators is assessed using a simulation study. Finally, a real life example is considered to illustrate the application and development of the inference methods.E-Bayesian and robust Bayesian estimation and prediction for the exponential distribution based on record values
https://jirss.irstat.ir/article_703326.html
&lrm;This article deals with the problem of E-Bayesian and robust Bayesian&nbsp; estimation and prediction&nbsp; in the&nbsp; exponential distribution &lrm;on the basis of record observations under the squared log error loss function. &lrm;&lrm;The &lrm;E-Bayesian&nbsp; and robust Bayesian estimators of the scale parameter are computed and their performances are investigated using a simulation study&lrm;. &lrm;We extend &lrm;the idea of &lrm;E-Bayesian&nbsp; estimation to the E-Bayesian&nbsp; prediction of future record observation and perform a simulation study using a prequential analysis for comparison of proposed E-Bayesian and robust Bayesian predictors. Two real data sets are analyzed for illustrating the estimation and prediction results.A bivariate process based maintenance model for two-component parallel systems
https://jirss.irstat.ir/article_706005.html
This paper proposes a bivariate process-based model for maintenance and inspection planning of a parallel system consisting of two components whose states evolve in one of three possible states: normal (0), satisfactory (1) and failure (2). The changes of states driven by a non-homogeneous Markov process are detected only by inspections and repair actions are determined by the observed state of the bivariate process. Outperforming maintenance strategies and other classical maintenance policies, the paper aims at minimizing the long-run average maintenance cost per unit time by deriving optimal inspection intervals and a preventive replacement threshold. A numerical example is given to illustrate the proposed model and examine the response of the optimal solutions to system parameters. The model explored here provides the framework for further developments.Stochastic comparisons on the residual lifetimes of series systems with arbitrary components using copulas
https://jirss.irstat.ir/article_706591.html
In this paper, we consider series systems consisting of arbitrary dependent components. We study the residual lifetimes of such systems based on copulas family from a new point of view. First, we extract a new explicit expression for the reliability functions of residual lifetimes of the systems. In following we give some stochastic ordering properties for the residual lifetimes of series systems based on the dependence structure of components and corresponding the mean functions. The results are expanded for series systems having used components of age $t&gt;0$. Subsequently, the problem of the stochastic comparison of a series system having used components and a used series system has been considered. To show the application of results, we provide some numerical examples. Finally, we present some dependence properties of the residual lifetimes of series system based on the properties of the lifetimes of components.First-Order Spatial Gegenbauer Autoregressive (SGAR(1,1)) Model and some of its Properties
https://jirss.irstat.ir/article_706592.html
In this paper, we extend the idea of Gegenbauer process in the spatial domain by introducing a more general parameter and call this model as Spatial Gegenbauer Autoregressive (SGAR(1,1)) model.
The spectral density and autocovariance functions of the model are introduced. The Yajima estimators of the Gegenbauer parameters, the log-periodogram regression estimators of the memory parameters and the Whittle's estimators of all parameters are discussed. The performance of these estimators are evaluated through a simulation study.Bayesian Premium Estimators for Pareto Distribution in the Presence of outliers
https://jirss.irstat.ir/article_706593.html
We propose the Pareto distribution in the presence of outliers based on the Dixit&nbsp;model. We consider the estimation of the Bayesian Premium under squared error loss&nbsp;function (symmetric), linear exponential, and entropy loss function (asymmetric), using&nbsp;informative and non-informative priors. We use the Lindley approximation and Markov&nbsp;Chain Monte Carlo methods such as the importance sampling procedure. Finally, the&nbsp;results are analyzed by using simulation studies.ARMA Autocorrelation Analysis: Parameter Estimation and Goodness of Fit Test
https://jirss.irstat.ir/article_706993.html
The celebrated Ljung-Box residual analysis is a widely used method in time series for the parameter estimation and the goodness of fit test for the ARMA time series models. The question is whether the autocorrelation function of the fitted ARMA model for an observed time series, at different lags, in the Ljung-Box estimation method, is close to the correlogram of observed series. The answer indeed is not affirmative. In this article, firstly, we present a new procedure in solving the Yule-Walker equations for the exact computation of the autocorrelation functions of ARMA(p; q) models. Secondly, we provided a goodness of fit procedure using the limiting distribution of the the sample correlation function. Thirdly, we establish a new parameters estimation method based on examining the model autocorrelation function against the series autocorrelation coefficients. The effectiveness of the procedure is brought into sight using simulated data.Characterizations of some discrete distributions and upper bounds on discrete residual varentropy
https://jirss.irstat.ir/article_706994.html
In this article, we obtain an upper bound for the variance of a function of the residual life randomvariable for discrete lifetime distributions. As a special case, we find an upper bound for residualvarentropy. Moreover we characterize some discrete distributions by Cauchy-Schwarz inequality. We alsoget new expressions, bounds and stochastic comparisons involving measures in reliability and informationtheory.&nbsp;Stochastic comparison of Hariss family distributions with fixed and randomized tilt parameter
https://jirss.irstat.ir/article_707183.html
In this paper, we stochastically compare Harris family distributions having random tilt parameter with Harris family distributions having fixed tilt parameter. We also study certain preservation properties of mixtures of Harris family of distributions with regards to their baseline distributions. Comparison tools are various types of orderings, such as the usual, shifted, proportional and shifted proportional stochastic orderings. Several previous findings, regarding Marshall-Olkin family, follow as special cases of our results. We shall also fit a new Harris model to a real data set to illustrate the usefulness of our comparisons.Ruin Probabilities for Two Insurance Risk Models with Asymptotically Independent and Dependent Classes
https://jirss.irstat.ir/article_707215.html
This paper presents two new insurance risk models for the analysis of time ruin probabilities. We firstly restrict ourselves to the classical risk model where the individual net losses are heavy tailed with common distribution function and equilibrium distribution function of the insurance risks when the nonnegative random premium income rates are flexible quantities which maybe change every year. Under certain technical assumptions, some asymptotic expansions and recursive formulas are obtained for the finite time and infinite time ruin probabilities. In the second risk model, we consider a new dependent class between the claim amounts, i.e. for a fixed period&nbsp; i, i=1, 2, ..., it is assumed that the different classes of the portfolio business are dependent and compute the finite time ruin probability based on the discretization of the distribution function. We present some numerical examples in the portfolio of business and show that the value of ruin probability increases as dependence level increases. Also, the sensitivity of the results are investigated with respect to the parameters of Weibull and Exponential distributions.Large Orderings of Extreme Order Statistics with Archimedean Copula and Powered Gompertz Random Variables
https://jirss.irstat.ir/article_707216.html
Bathtub-shaped failure rate distributions are of special interest in reliability theory, survival analysis, and many other fields. The so-called power Gompertz distribution is one of the popular lifetime distributions that possesses the bathtub-shaped failure rate function. In this paper, we study some stochastic comparison results for extreme order statistics from dependent powered Gompertz distributed random variables under Archimedean copula. The study has been carried out in the sense of the usual stochastic order and the dispersive order.Construction of generalized Dirichlet process distributions via Polya urn and Gibbs sampling
https://jirss.irstat.ir/article_707638.html
Bayesian nonparametric inference is increasingly demanding in statistical modeling due to incorporating flexible prior processes in complex data analysis and allowing analysts to achieve the most information from an infinite mixture of stochastic priors. The Dirichlet process mixture model can facilitate Bayesian computational aspects via conventional stochastic schemes. This paper represents the P\&#039;{o}lya urn scheme for the generalized Dirichlet process (GDP). It utilizes the partition analysis to construct the joint distribution of a random sample from the GDP as a mixture prior distribution of countable components. Using permutation theory, we present the components&#039; weights in a computationally accessible manner to make the resulting joint prior equation applicable. The advantages of our findings include tractable algebraic operations that lead to closed-form equations. The paper recommends the P\&#039;{o}lya urn Gibbs sampler algorithm, derives full conditional posterior distributions, and as an illustration, implements the algorithm for fitting some popular statistical models in nonparametric Bayesian settings.An improved two-stage randomized response model for estimating the mean of a quantitative sensitive random variable
https://jirss.irstat.ir/article_707639.html
This paper introduces a new two-stage randomized response model for estimating the mean of a sensitive quantitative random variable. The proposed model is obtained for both simple and stratified random sampling. The efficiency of the proposed estimator, under both sampling schemes, is investigated with respect to various estimators and it is found to be more efficient. Moreover, a new measure for evaluating the performance of any randomized response estimator is introduced. The measure considers the relative efficiency of the randomized response estimator compared to the sample mean, and the privacy protection it offers. The performance of the proposed estimator is examined using the new measure and it is found to have an overall better performance than its rival estimators. A real data example is also examined using the proposed model and various models from literature.Inference on Quantiles of Several Exponential Populations with a Common Location: Hypothesis Testing and Interval Estimation
https://jirss.irstat.ir/article_707640.html
This article deals with the problems of testing the hypothesis on and interval estimation of the $p$-th quantile, $\xi = \mu+\eta \sigma_{1},$ where $\eta=-\log(1-p);$ $0&lt;p&lt;1$ of the first population, when samples are available from several exponential populations with a common location and possibly different scale parameters. Several test procedures, such as tests using a generalized variable approach, tests based on parametric bootstrap method, and tests using a computational approach to test the null hypothesis against a suitable alternative, have been proposed. Several interval estimators for the quantile $\xi,$ such as confidence intervals based on generalized variable approach, parametric bootstrap approach and Bayesian intervals using Markov chain Monte Carlo (MCMC) method have been proposed. The confidence intervals are compared through their coverage probabilities and average lengths, whereas the test statistics are compared in terms of powers and sizes numerically. The application of our model problem has been shown using real-life data sets, and conclusions have been made there.Statistical Relationship between Quantitative and Dichotomous Variables: Student’s Test and Moving Average Approach
https://jirss.irstat.ir/article_707641.html
A new technique is proposed for evaluating the statistical relationship between a quantitative variable Y and a dichotomous variable X assuming two values: X=0 and X=1. The technique is based on the division of the quantitative variable Y into strata by the moving average technique and computation of average values in the strata for the variables Y and X. Stratification turns the dichotomous variable X into a quantitative one. Once the variable X has been transformed in this way, the statistical relationship between Y and X may be analyzed by linear regression and by analysis of variance. Thus, the technique proposed expands the range of methods available for analyzing statistical relationships between quantitative and dichotomous variables. Specific examples are used to compare the moving average technique with the t-test for symmetric (normal) and asymmetric distributions of quantitative variable Y. It is shown that the statistical relationship between stratified Y and X can be strongly different for a symmetrically (normally) distributed variable Y.On Zero-inflated Extended Alternative Hyper Poisson Distribution and its Applications
https://jirss.irstat.ir/article_707642.html
In this paper we propose a zero-inflated version of the extended alternative hyper-Poisson distribution of Kumar and Nair (2013b) and investigate some of its important properties and applications. We derive expressions for its probability generating function, mean, variance, etc. along with recursion formulae for probabilities, raw moments and factorial moments. The identifiability condition of the model is also derived. The estimation of the parameters of the distribution is also attempted and it has been fitted to certain real life data sets for highlighting its practical relevance. Further, generalized likelihood ratio test procedure is applied for examining the significance of the parameters of the model and a simulation study is conducted for assessing the performance of the maximum likelihood estimators of the parameters of the distribution.Inference on Generalized Inverse Lindley distribution under Progressive Hybrid censoring scheme
https://jirss.irstat.ir/article_707643.html
This article delineates the implementation of Product of spacings under Progressive Hybrid Type-I censoring with binomial removals for the Generalized Inverse Lindley distribution. Both point and interval estimates of the parameters have been obtained under classical as well as Bayesian paradigm using product of spacings. The proposed estimators can be used in lieu of Maximum likelihood estimator and usual Bayes estimator based on likelihood function which is corroborated by a comparative simulation study. The Bayesian estimation is performed under the assumption of squared error loss function. The implicit integrals involved in the process are evaluated using Metropolis-Hastings algorithm within Gibbs sampler. We have also derived the expected total time to test statistic for the specified censoring scheme. The applicability of the proposed methodology is demonstrated by analysing a real data set of active repair times for an airborne communication transceiver.