Journal of the Iranian Statistical Society
https://jirss.irstat.ir/
Journal of the Iranian Statistical Societyendaily1Thu, 01 Dec 2022 00:00:00 +0330Thu, 01 Dec 2022 00:00:00 +0330ARMA 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(p,q) 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.Inference on Generalized Inverse Lindley Distribution under Progressive Hybrid Censoring Scheme
https://jirss.irstat.ir/article_707643.html
This article delineates the implementation of the 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 paradigms using the product of spacings. The proposed estimators can be used in lieu of maximum likelihood as well as 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 analyzing a real data set of active repair times for an airborne communication transceiver.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. Moreover, we give some stochastic ordering properties for the residual lifetimes of series systems based on the dependence structure of the components and the corresponding 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.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, 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.The 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. This paper represents the Polya 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' 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 Polya urn Gibbs sampler algorithm, derive full conditional posterior distributions, and as an illustration, implement the algorithm for fitting some popular statistical models in nonparametric Bayesian settings.E-Bayesian and Robust Bayesian Estimation and Prediction for the Exponential Distribution based on Record Values
https://jirss.irstat.ir/article_703326.html
This article deals with the problem of E-Bayesian and robust Bayesian estimation and prediction in the exponential distribution on the basis of record observations under the squared log error loss function. The E-Bayesian and robust Bayesian estimators of the scale parameter are computed and their performances are investigated using a simulation study. We extend the idea of E-Bayesian estimation to the E-Bayesian 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.Ruin Probabilities for Two Risk Models with Asymptotically Independent and Dependent Classes
https://jirss.irstat.ir/article_707215.html
This paper presents two new insurance risk models for analyzing the ruin probabilities. Firstly, we restrict ourselves to the classical risk model contains heavy-tailed distribution of individual net losses and changeable premium income rates. Under certain technical assumptions, some asymptotic expansions and recursive formulas are obtained for the ruin probabilities. In the second risk model, we assume 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. Moreover, the sensitivity of the results are investigated with respect to the parameters of&nbsp; Weibull and Exponential distributions.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 comparisons 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.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.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 random variable for discrete lifetime distributions. As a special case, we find an upper bound for residual varentropy. Moreover we characterize some discrete distributions by Cauchy-Schwarz inequality. We also get new expressions, bounds and stochastic comparisons involving measures in reliability and information theory.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.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.Developing flexible classes of distributions to account for both skewness and bimodality
https://jirss.irstat.ir/article_708400.html
We develop two novel approaches for constructing flexible skewed and bimodal distributions that can effectively&nbsp;generalize classical symmetric distributions. We illustrate the application of introduced techniques by extending normal, student-t, and Laplace distributions. We also study the properties of the newly&nbsp;constructed distributions. The method of maximum likelihood is proposed for estimating the model parameters.&nbsp;Furthermore, the application of new distributions is represented using real-life data.
We develop two novel approaches for constructing flexible skewed and bimodal distributions that can effectively&nbsp;generalize classical symmetric distributions. We illustrate the application of introduced techniques by extending normal, student-t, and Laplace distributions. We also study the properties of the newly&nbsp;constructed distributions. The method of maximum likelihood is proposed for estimating the model parameters.&nbsp;Furthermore, the application of new distributions is represented using real-life data.Preferences of women for maternal healthcare services in the Upper East Region: A stated choice experiment
https://jirss.irstat.ir/article_711320.html
This research examined preferences of women for maternal health service locations in Ghana&rsquo;s Upper East Region. Analyzing data from 200 respondents with diverse sociodemographic backgrounds, the research emphasized key factors such as availability of drugs and equipment, the facility environment, provider attitudes, distance to health facilities, and referrals at healthcare facilities. By using a panel mixed logit model, the study demonstrated the significant impact of these attributes on women&rsquo;s choices, except for the cost of delivery services, which did not exhibit significance. Sociodemographic variables like age, employment status, marital status, religion, education, and place of last delivery also impacted preferences. The availability of drugs and equipment emerged as the most influential attribute across different groups. The study highlights the importance of understanding women&rsquo;s preferences and providing high-quality, patient-centered care to promote positive maternal health outcomes in the region. Policymakers should
thus consider these factors to enhance healthcare facility utilization, reduce maternal mortality rates, and improve maternal health outcomes.Practical Learning Directed Acyclic Graphs With General Noise Assumptions
https://jirss.irstat.ir/article_711656.html
Directed Acyclic Graphs are investigated focusing on learning the coefficient matrix via continuous optimization.
We have provided three learning strategies and their corresponding improvements in comparison with former algorithms using some numerical illustrations.
Each method is widely introduced and its corresponding concepts are also studied.
We have extended, the learning assumptions for each strategy.
Lots of preliminary assumptions including normality of noises, and independent and identically distributed errors are removed and with these general considerations, the learning methods are even improved than some existing methods.
Furthermore, the number of new criteria that can evaluate the learning processes are given and throughout simulation studies are analyzed.
Their sensitivity analysis is also presented which can be useful due to the learning power of any presented strategy.
Finally, some further discussions are introduced as guidance for future works.Information measures for record values and their concomitants under iterated FGM bivariate distribution
https://jirss.irstat.ir/article_712344.html
Let $\{(X_i,Y_i), i\geq1\}$ be a sequence of bivariate random variables (RVs)
from a continuous distribution. If $\{R_{n}, n\geq1\}$ is the sequence of record
values in the sequence $\{X_i\},$ then the RV $Y_i,$ which corresponds to $R_n$ is called the concomitant of the $n$th-record, denoted by $R_{[n]}.$ In this paper, we study the Shannon&#039;s entropy of $R_{[n]}$ and $(R_{n},R_{[n]}),$ under iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate distribution. In addition, we find the Kullback-Leibler distance (K-L distance) between $R_{[n]}$ and $R_{n}.$ Moreover, we study the Fisher information matrix (FIM) for record values and their concomitants about the shape-parameter vector of IFGM bivariate distribution. Also, we study the relative efficiency-matrix of that vector-estimator of the shape-parameter vector whose covariance matrix is equal to Cram\&#039;{e}r-Rao lower bound, based on record values and their concomitants and i.i.d observations. In addition, the Fisher information number (FIN) of $R_{[n]}$ is derived. Finally, we evaluate the FI about the mean of exponential distribution in the concomitants of record values.