Journal of Statistical Modelling: Theory and ApplicationsJournal of Statistical Modelling: Theory and Applications
http://jsm.yazd.ac.ir/
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http://jsm.yazd.ac.ir/
Feed provided by Journal of Statistical Modelling: Theory and Applications. Click to visit.Computational approach test in one-way fixed effects ANOVA models of log-normal samples
http://jsm.yazd.ac.ir/article_1698_143.html
We apply a recently developed computational approach test (CAT) to the one-way fixed effects ANOVA models of log-normal data with unequal variances. The merits of the proposed test are numerically compared with the existing tests - the James second order test, the Welch test and the Alexander-Govern test - with respect to their sizes and powers in different combinations of parameters and various sample sizes. The simulation results demonstrate that the proposed method is satisfactory: its type I error probability is very close to the nominal level. We illustrate these approaches using a real example.Sun, 31 Dec 2017 20:30:00 +0100Improved maximum likelihood estimation of parameters in the Maxwell distribution
http://jsm.yazd.ac.ir/article_1731_0.html
Maximum likelihood estimators are usually biased. The first order bias term of the maximum likelihood estimators can be large for a small or medium sample size, and this bias may have a significant effect on distribution performance. Different methods may be used to reduce this bias. These methods have inspired many scholars to study this field over the past years, but the use of Bartlett’s method requires the expected value of third power derivatives of the likelihood function. Consequently, because this quantity (the expected value of third power derivatives of the likelihood function) is not necessarily calculable in some distributions, in this paper we propose a new method based on algebraic approximation of the maximum likelihood estimator bias which needless the expected value of third power derivatives of the likelihood function. In addition, as an application of this method, we will consider a bias correction for estimating parameters of Maxwell distribution.Mon, 02 Mar 2020 20:30:00 +0100Modeling insurance data using generalized gamma regression
http://jsm.yazd.ac.ir/article_1733_0.html
The generalized gamma (GG) is a flexible distribution in statistical literature with the special cases of exponential, gamma, Weibull and lognormal distributions. This paper investigates the GG additive model for modeling hospital claim costs. In comparison to other models, the GG is more flexible and has a better performance in modeling positively skewed data. The proposed model was fitted to the hospital costs data from the nationwide inpatient sample of the health care cost and utilization project, a nationwide survey of hospital costs conducted by the U.S. Agency for healthcare research and quality. The results indicate that the claim cost is affected by the given explanatory variables and based on the AIC and BIC criteria, the GG has a better performance for the given data compared to the alternatives.Mon, 02 Mar 2020 20:30:00 +0100A new extended alpha power transformed family of distributions: properties and applications
http://jsm.yazd.ac.ir/article_1706_143.html
In this paper, a new method has been proposed to introduce an extra parameter to a family of lifetime distributions for more flexibility. A special sub-case has been considered in details namely; two parameters Weibull distribution. Various mathematical properties of the proposed distribution, including explicit expressions for the moments, quantile, moment generating function, residual life, mean residual life and order statistics are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. A simulation study is conducted to evaluate the performances of these estimators. For the illustrative purposes, two data sets havebeen analyzed to show how the proposed model work in practice.Sun, 31 Dec 2017 20:30:00 +0100Modeling spatial patterns and species associations in a Hyrcanian forest using a multivariate ...
http://jsm.yazd.ac.ir/article_1732_0.html
This paper aims to conduct a model-based analysis of the spatial patterns of three tree species in a Hyrcanian forest and investigate their associations. There are many known and unknown mechanisms that influence the spatial forest structure and species associations. These complex and mainly unobservable mechanisms can be modeled by hidden Gaussian random fields and log-Gaussian Cox process models are appropriate for linking them to the spatial patterns of tree species. We consider a multivariate log-Gaussian Cox process model that can take into account the overall mixed effects of all influential factors on spatial distributions of species and quantify species associations in terms of some parameters. This construction provides a suitable framework for modeling and analyzing spatial patterns of several species. We also discuss modeling tree diameters, parameter estimation and goodness of fit methods and apply them to the data. Results from fitting the model to the data show that there is a significant negative association between two light-demanding species. Finally, a Gamma intensity-dependent model is considered to model spatial correlation in tree diameters of one of the species.Mon, 02 Mar 2020 20:30:00 +0100The exponentiated odd log-logistic family of distributions: properties and applications
http://jsm.yazd.ac.ir/article_1707_143.html
Based on the generalized log-logistic family (Gleaton and Lynch (2006)) of distributions, we propose a new family of continuous distributions with two extra shape parameters called the exponentiated odd log-logistic family. It extends the class of exponentiated distributions, odd log-logistic family (Gleaton and Lynch (2006)) and any continuous distribution by adding two shape parameters. Some special cases of this family are discussed. We investigate the shapes of the density and hazard rate functions. The proposed family has also tractable properties such as various explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, extreme values and order statistics, which hold for any baseline model. The model parameters are estimated by maximum likelihood and the usefulness of the new family is illustrated by means of three real data sets.Sun, 31 Dec 2017 20:30:00 +0100Bayesian D-optimal design for a quadratic beta regression model with a known nuisance parameter ...
http://jsm.yazd.ac.ir/article_1771_0.html
One of the practical and important issue in statistics is the fitness of regression models. Optimal design is a way to obtain suitable fitness of this type of models. In addition, we need to use some criteria for attaining optimal design in regression models. The D-optimality criterion is one of the most famous criteria which is used here. An appropriate method to obtain the optimal designs is the Bayesian method that need to the prior distribution for the parameters of the model (coefficient regression). In this paper, by using Bayesian methods, D-optimal designs are obtained for quadratic beta regression model. Also, uniform and normal distributions are considered as the prior distributions and obtained results are analyzed.Sun, 29 Mar 2020 19:30:00 +0100Comparisons for series and parallel systems with discrete Weibull components via separate ...
http://jsm.yazd.ac.ir/article_1708_143.html
‎In this paper‎, ‎we obtain the usual stochastic order of series and parallel systems comprising heterogeneous discrete Weibull (DW) components‎. ‎Suppose X1,...,Xn and Y1,...,Yn denote the independent component¢s lifetimes of two systems such that Xi ~ DW(bi‎, ‎pi) and Yi ~ DW(b*i‎, ‎p*i), i=1,...,n. We obtain the usual stochastic order between series systems‎ ‎when the vector boldsymbolb is switched to the vector b*with respect to the majorization order‎, ‎and when the vector log (1-p) is switched to the vector log (1-p*) in the sense of the weak supermajorization order‎. ‎We also discuss the usual stochastic order between series systems by using the unordered majorization between the vectors log(1-p) and log (1-p*), and the p-majorization order between the parameters boldsymbolb and b*. It is also shown that the usual stochastic order between parallel systems comprising heterogeneous discrete Weibull components when the vector log p is switched to the vector log p*in the sense of the weak supermajorization order‎. ‎These results enable us to find some lower bounds for the survival functions of a series and parallel systems consisting of independent heterogeneous discrete Weibull components.Sun, 31 Dec 2017 20:30:00 +0100Interval estimation of stress-strength reliability parameter for exponential-inverted ...
http://jsm.yazd.ac.ir/article_1785_0.html
This paper introduces the problem of interval estimation for stress strength reliability parameter P(X<Y)‎, ‎where random variables X and Y stand for stress and strength‎, ‎respectively‎. ‎In most of the research papers‎, ‎the authors assumed that X and Y come from the same family of distribution‎. ‎By taking into account some situations arise‎, ‎in this paper we assume that X and Y follow exponential and inverted exponential distributions‎, ‎respectively‎. ‎Our goal is to construct a confidence interval for reliability parameter in this model by using some (approximately) exact and strong methods such as bootstrap‎, ‎generalized and highest posterior distribution approaches‎. ‎Also‎, ‎we compare these methods by means of the expected length and coverage probability criteria‎. ‎Finally‎, ‎a real data set is given and we apply the above methods of estimation on it to inference about the parameter of interest.Tue, 07 Apr 2020 19:30:00 +0100Recurrence relations for moments of progressively Type-II censored order statistics from a ...
http://jsm.yazd.ac.ir/article_1709_143.html
In this paper, some recurrence relations are presented for the single and product moments of progressively Type-II right censored order statistics from a Pareto distribution. These relations are obtained for a progressively censored sample from Pareto distribution with fixed and random removals, where in the random case, the number of units removed at each failure time follows a binomial distribution. In addition,Thomas-Wilson’s Mixture Formula for Moments are obtained with with fixed and random removals. Finally, a numerical study is carried out to compare real and simulation results based on biases and MSEs of the expected termination time.Sun, 31 Dec 2017 20:30:00 +0100A new discrete distribution based on geometric odds ratio
http://jsm.yazd.ac.ir/article_1825_0.html
In this paper, a new discrete distribution is studied based on geometric odds ratio. This new distribution has three parameters and can be a unimodal or a bimodal discrete distribution. Some important distributional properties are studied. For example, moments, the behaviour of the hazard rate function, stochastic orders, mixing processes, infinite divisibility, Rényi and Shannon entropies and the distributions of order statistics are investigated. We will see that the hazard rate function of the new discrete distribution can be monotonically increasing and decreasing and bathtub-shaped. The parameters of the distribution are estimated by the maximum likelihood method, and a real data set is analyzed in order to show the effectiveness of the model.Sat, 27 Jun 2020 19:30:00 +0100Mathematics of evidences in dynamic systems with exponential component lifetimes and optimal ...
http://jsm.yazd.ac.ir/article_1710_143.html
In this paper, statistical evidences in lifetimes of sequential r-out-of-n systems, which are modelled by the concept of sequential order statistics (SOS), coming from homogeneous exponential populations are considered. Weak and misleading evidences in SOS for hypotheses about the population parameter are derived in explicit expressions and their behaviours with respect to the model parameters are studied in details. Optimal sample sizes given a minimum desired level for the decisive and the correct probabilities are provided. It is shown that the optimal sample size does not depend on some model parameters.Sun, 31 Dec 2017 20:30:00 +0100Characterizations on the basis of cumulative residual entropy of sequential order statistics
http://jsm.yazd.ac.ir/article_1711_143.html
This article deals with the problem of characterizing the parent distribution on the basis of the cumulative residual entropy of sequential order statistics under a conditional proportional hazard rates model. It is shown that the equality of the cumulative residual entropy in the first sequential order statistics determines uniquely the parent distribution. Subsequently, we characterize the Weibull distribution on the basis of the ratio of the cumulative residual entropy of first sequential order statistics to the corresponding mean. Also, we consider characterizations based on the dynamic cumulative residual entropy and derive some bounds for the cumulative residual entropy of residual lifetime of the sequential order statistics.Sun, 31 Dec 2017 20:30:00 +0100On construction confidence interval for linear combination means of several heterogeneous ...
http://jsm.yazd.ac.ir/article_1712_143.html
We consider the problem of constructing confidence interval for linear combination of the means of several log-normal distributions. We apply the generalized confidence interval (GCI) approach and the method of variance estimate recovery (MOVER) to construct confidence intervals for the linear combination of log-normal means. We then compare the performances of the proposed confidence intervals via a simulation study and a real data example. Simulation results show that our proposed MOVER and GCI confidence intervals can be recommended generally for different sample sizes and different number of groups.Sun, 31 Dec 2017 20:30:00 +0100Point prediction for the proportional hazards family based on progressive Type-II censoring ...
http://jsm.yazd.ac.ir/article_1713_143.html
‎In this paper‎, ‎some different predictors are presented for failure times of units censored in a progressively censored sample from proportional hazard rate models‎, ‎where the number of units removed at each failure time follows a binomial distribution‎. ‎The maximum likelihood predictors‎, ‎best unbiased predictors and conditional median predictors are derived‎. ‎Also‎, ‎the Bayesian point predictors are investigated for the failure times of units with the three common loss function‎. ‎Finally‎, ‎a numerical example and a Monte Carlo simulation study are carried out to compare all the prediction‎ ‎methods discussed in this paper.Sun, 31 Dec 2017 20:30:00 +0100A new simple and powerful normality test for progressively Type-II censored data
http://jsm.yazd.ac.ir/article_1714_143.html
In this paper, a new goodness-of-fit test for a location-scale family based on progressively Type-II censored order statistics is proposed. Using Monte Carlo simulation studies, the present researchers have observed that the proposed test for normality is consistent and quite powerful in comparison with some existing goodness-of-fit tests based on progressively Type-II censored data. Also, the new test statistic for a realdata set is used and the results show that the new proposed test statistic performs well.Sun, 31 Dec 2017 20:30:00 +0100Preliminary test estimation in Rayleigh distribution under a squared-log error loss
http://jsm.yazd.ac.ir/article_1715_143.html
The problem of pretest estimation in Rayleigh type-II censored data under the squared-log error loss (SLEL) is considered. The risk-unbiased estimator is derived and its risk is computed under the SLEL. The pretest estimator based on a point guess about the parameter of interest is constructed and the bias and risk is computed. A comparison study is performed between the pretest estimator and the risk-unbiased estimator. The optimal level of significance and critical values of pretest is obtained using regret minimax method. A real data set is used for illustrative purposes.Sun, 31 Dec 2017 20:30:00 +0100On a measure of dependence and its application to ICA
http://jsm.yazd.ac.ir/article_1716_143.html
In this article we study a copula-based measure of‎ ‎dependence constructed based on the concept of average quadrant‎ ‎dependence‎. ‎The rank-based estimator of this index and its ‎asymptotic normality is investigated‎. ‎An algorithm for independent ‎component analysis is developed whose contrast function is the‎ ‎proposed dependence coefficient.Sun, 31 Dec 2017 20:30:00 +0100On some properties of transmuted Weibull distribution
http://jsm.yazd.ac.ir/article_1903_0.html
A new generalized version of the Weibull distribution, which is called the perturbed Weibull distribution, is introduced in this paper. The present distribution provide enough flexibility for analyzing different types of data with increasing, decreasing, constant, bathtub shaped, unimodal, increasing-decreasing-increasing and decreasing-increasing-decreasing hazard functions in comparing with former extensions of the Weibull distribution. We study its properties including servival and hazard functions, moments, moment generating and characteristic functions, quantiles and Renyi entropy. Estimation of parameters using the methods of moment and maximum likelihood is obtained. We show the consistency of the moments and maximum likelihood estimators using some simulation study. Finally, the flexibility of the new distribution is illustrated in an application to two real data sets.Wed, 16 Sep 2020 19:30:00 +0100The odd generalized half-logistic Weibull-G family of distributions: properties and applications
http://jsm.yazd.ac.ir/article_1904_0.html
We propose a new generalized family of distributions called the odd generalized half logistic Weibull-G family of distributions. We also considered some special cases when the baseline distribution are uniform, Weibull and normal distributions. Structural properties of the new family of distributions including expansion of density, distribution of order statistics, Rényi entropy, moments, probability weighted moments, quantile and generating functions, and maximum likelihood estimates were derived. A characterization based on conditional expectation is presented. A simulation study to examine efficiency of the maximum likelihood estimates is also conducted. Finally, a real data example is presented to illustrate the applicability and usefulness of the proposed model.Thu, 17 Sep 2020 19:30:00 +0100On the weighted dynamic cumulative residual entropy and dynamic cumulative past entropy with ...
http://jsm.yazd.ac.ir/article_1923_0.html
The main measure of the uncertainty contained in random variable X is the Shannon entropy H(X) = −E(log(f(X)). The cumulative entropy is an information measure which is alternative to the Shannon entropy and is connected with reliability theory. The cumulative residual entropy (CRE) introduced by Rao et al. (2004) is a generalized measure of uncertainty which is applied in reliability. Asadi and Zohrevand (2007) defined a dynamic version of the CRE by ε(X,t). In this paper, weighted residual entropy and weighted cumulative residual entropy are discussed. The properties of weighted entropy, cumulative residual entropy, weighted residual entropy, weighted cumulative residual entropy, weighted past entropy, weighted cumulative past entropy, dynamic cumulative residual entropy, dynamic cumulative past entropy, are also given.Wed, 14 Oct 2020 20:30:00 +0100