Journal of Statistical Modelling: Theory and Applications
Volume:2 Issue: 1, Winter and Spring 2021

In this paper‎, ‎we introduce the hyperbolic tan-X family of distributions as a new statistical distribution defined by a trigonometric function‎. ‎Some properties and applications of the new family are investigated in some detail‎. ‎A characterization theorem extending the new class of statistical distributions is also considered‎. ‎Avenues for further research are also presented‎.

A new family of distributions referred to as the exponentiated half logistic odd Weibull-Topp-Leone-G family of distributions is developed. We derive statistical properties of the new family of distributions. The distribution can be expressed as a linear combination of the exponentiated-G distribution. Five special cases for the new family of distributions are also presented. Estimation and Monte Carlo simulation study was also conducted. Two real data examples for a selected special case are also presented.

Degradation modeling is an effective approach for reliability assessment and predicting of remaining useful life in order to investigate the relation between failure time and degradation of a system or unit. The possibility of an association between degradation of the unit during the time and the effects of covariates on degradation processes should be taken into account in the model to improve the explanatory capabilities of degradation models. Sometimes, the exact amount of degradation could not be observed because of time, cost, and measurement tools limitations. Therefore, approximate degradation values can be compared with a critical threshold. In this paper, the degradation processes modeled with a generalized linear mixed-effect model in order to take into account the correlation between times. Also, maximum likelihood estimation and Bayesian estimate of parameters are derived.

The shock models have attracted a great deal of attention because of their important role in engineering systems. If the time between two successive shocks is less than the pre-defined threshold δ, the system fails, which is called the δ-shock model. In this article, we studied the generalized δ-shock model with two types of arrival shocks under a Polya process which has dependent interarrival times. The survival function and the mean lifetime of this system are obtained. Finally, some illustrative examples are presented.

Measuring the total contribution of the components in a system is useful for various goals. Therefore, several component importance measures have been introduced in the literature. One of the well-known measures is the Birnbaum component importance measure. This paper concentrates on obtaining the Birnbaum component importance of the components of a consecutive-(k, k)-out-of-n:F system having two dependent subcomponents. A numerical example is also presented to illustrate the obtained results.

In this article‎, ‎we consider the estimation of the parameters and reliability characteristics of Kumaraswamy distribution using progressive first failure censored samples‎. ‎First‎, ‎we derive the maximum likelihood estimates using an expectation-maximization algorithm and compute the observed information of the parameters that can be used for constructing asymptotic confidence intervals‎. ‎We also compute the Bayes estimates of the parameters using Lindley approximation as well as the Metropolis-Hastings algorithm‎. ‎Furthermore‎, ‎we derive the highest posterior density credible intervals‎. ‎Simulation studies are conducted to evaluate the performance of the point and interval estimators‎. ‎Finally‎, ‎two examples of real data sets are provided to illustrate the proposed procedures.

We develop a generalized distribution, namely, exponentiated half logistic log-logistic Weibull distribution. Several structural properties of the distribution including expansion of density, distribution of order statistics, Rényi entropy, moments, probability weighted moments, quantile function, generating function, and maximum likelihood estimates were derived. A simulation study to examine the consistency of the maximum likelihood estimates was conducted. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed model.

‎A new generalized family of distributions called the odd power generalized Weibull-G family of distributions is developed‎. Some ‎properties of the new family of distributions including quantile function‎, ‎moments‎, ‎incomplete and probability weighted moments‎, ‎distribution of the order statistics and Renyi entropy are derived‎. ‎Estimation of model parameters using maximum likelihood estimation technique and simulation study to examine the bias and mean square error are discussed‎. ‎Applications to real data sets to illustrate the applicability of the generalized family of distributions is also given‎.

In survival data, it is typical for survival times to be clustered or depend on some unobserved covariates. This can be due to geographical clustering, subjects sharing common genes, specific socioeconomic level, or hereditary and racial characteristics, and other predisposition that cannot be measured and observed directly. Adjusting the effects of these unknown factors on the survival functions is necessary for the independence of survival times and the explanatory variables. The aim of this study is to introduce and compare Cox models with parametric and non-parametric shared frailty on brain stroke survival data. The results showed that non-parametric frailty model has better fitting than parametric distributions (AIC=4686 and BIC=4684), especially when the exact parametric distribution is not known. According to the results of best model, following variables were statistical significant; BMI (HR=0.97, P=0.045); Age (HR=1.04, p <0.001); HDL (HR=1.01, p <0.001); LDL (HR=0.99, p <0.001); Hyperlipidemia (HR=0.72, p <0.014). The nonparametric frailty is desirable, due to potential misspecification of the parametric form and as a method for detecting clusters of groups with similar frailties.

A new generalized family of distributions called the Weibull Odd Burr III-G is introduced using the T-X transformation technique. Some of useful mathematical and statistical properties such as the hazard function, quantile function, moments, probability weighted moments, Rényi entropy, order statistics and stochastic orders are derived. The method of maximum likelihood estimation is used to estimate the model parameters. The usefulness of these family of distributions is demonstrated via simulated experiments and its special cases are applied to real life data sets to illustrate flexibility.

Missing data is a very common problem in all research fields. Case deletion is a simple way to handle incomplete data sets which could mislead to biased statistical results. A more reliable approach to handle missing values is imputation which allows covariate-dependent missing mechanism, as well. This paper aims to prepare guidance for researchers facing missing data problems by comparing various imputation methods including machine learning techniques, to achieve better results in supervised learning tasks. A benchmark dataset has experimented and the results are compared by applying popular classifiers over varying missing mechanisms and rates on this benchmark dataset.

In the presence of multicollinearity in the regression models‎, ‎the ordinary least squares estimator loses its performance‎. ‎Some solutions to reduce the effects of multicollinearity have been proposed‎, ‎including the application of biased estimators such as Liu estimate and estimation under linear restrictions‎. ‎But due to the Liu estimator being biased‎, ‎the Jackknife method has been introduced to reduce the bias‎. ‎In this paper‎, ‎we will examine the Jackknifed Liu estimator and propose a new estimator under stochastic linear restrictions namely stochastic restricted Jackknifed Liu estimator‎. ‎A simulation study is conducted to investigate the performance of this new estimator using two measures namely mean squared errors and absolute bias‎. ‎From simulation study results‎, ‎we find that the new estimator outperforms the OLS and Liu estimators‎, ‎and it is superior to both OLS and Liu estimators‎, ‎using the mean squared errors and absolute bias criteria‎.