Journal of Statistical Modelling: Theory and Applications
Volume:1 Issue: 1, Winter and Spring 2020

We apply a recently developed computational approach test 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.

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.

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.

‎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, ‎p i) 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.

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.

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.

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.

‎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.

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.

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.

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.

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.