The study of semiparametric families is useful because it provides methods of extending families for adding flexibility in fitting data. The main aim of this paper is to introduce a class of bivariate semiparametric families of distributions. One especial bivariate family of the introduced semiparametric families is discussed in details with its sub-models and different properties. In most of the cases the joint probability distribution, joint distribution and joint hazard functions can be expressed in compact forms. The maximum likelihood and Bayesian estimation are considered for the vector of the unknown parameters. For illustrative purposes a data set has been re-analyzed and the performances are quite satisfactory. A simulation study is performed to see the performances of the estimators.
This paper proposes the Topp-Leone Gompertz distribution; an extension of the Gompertz distribution for modeling real life time data. The new model is obtained by transforming the cumulative distribution function of the Gompertz random variable, while taking the Topp-Leone as the generator. Some statistical properties of the new distribution are derived. Maximum likelihood estimates of model parameters are also derived. A Monte Carlo simulation study is carried out to examine the accuracy of the maximum likelihood estimate of the distribution parameters. Two real data sets are used to illustrate the applicability of the new distribution, and the results show that the new distribution outperforms some related lifetime distributions.
One of the main features of bipolar disorder is repletion of relapse overtime. Many studies have focused on time-to-first relapse using the most popular Cox proportional hazard model which discards subsequent information on recurrent relapses. The aim of this study was to identify some risk factors of time-to-recurrent relapses in bipolar disorder inpatients by using appropriate recurrent event model. Data on 206 inpatients, available at Amanuel mental specialized hospital, were collected by reviewing the medical records from September 11, 2013 to March 12, 2019. Different extended cox proportional hazard models including AG, PWP-TT, PWP-GT and semiparametric shared gamma frailty models were used. R package FrailtyEM package used to fit semi-parametric shared gamma frailty models through EM algorithm. The mean age of the patients was 33.33 years. Within the study time, a total of 418 inpatient admissions (relapses) were registered for 206 inpatients. Among these admissions, about 49.3% of the patients had first relapse and 50.7% of the patients had more than one relapses. The likelihood test results indicated that the appropriate model is the gap-time based semi-parametric shared gamma frailty model and the important risk factors that have effect on time since the end of the most recent relapse to the start of the next relapses are marital status, substance abuse, employment status and residence. Recurrent relapse may be reduced by giving more intensive forms of treatment and creating awareness on each risk factor.
In this paper a new two-parameter distribution is proposed. This new model provides more flexibility to modeling data with increasing and bathtub hazard rate function. Several statistical and reliability properties of the proposed model are also presented in this paper, such as moments, moment generating function, order statistics and stress-strength reliability. The maximum likelihood estimators for the parameters are discussed as well as a bias corrective approach based on bootstrap techniques. A numerical simulation is carried out to examine the bias and the mean square error of the proposed estimators. Finally, an application using a real data set is presented to illustrate our model.
In this article, we introduce a class of distributions that have heavy tails as compared to Pareto distribution of third kind, which we termed as Heavy Tailed Pareto (HP) distribution. Various structural properties of the new distribution are derived. It is shown that HP distribution is in the domain of attraction of minimum of Weibull distribution. A representation of HP distribution in terms of Weibull random variable is obtained. Two characterizations of HP distribution are obtained. The method of maximum likelihood is used for estimation of model parameters and simulation results are presented to assess the performance of new model. Marshall-Olkin Heavy Tailed Pareto (MOHP) distribution is also introduced and some of its properties are studied. It is shown that MOHP distribution is geometric extreme stable. An autoregressive time series model with the new model as marginal distribution is developed and its properties are studied.