Journal of Data Science

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.

In this paper we introduce the generalized extended inverse Weibull finite failure software reliability growth model which includes both increasing/decreasing nature of the hazard function. The increasing/decreasing behavior of failure occurrence rate fault is taken into account by the hazard of the generalized extended inverse Weibull distribution. We proposed a finite failure non-homogeneous Poisson process (NHPP) software reliability growth model and obtain unknown model parameters using the maximum likelihood method for interval domain data. Illustrations have been given to estimate the parameters using standard data sets taken from actual software projects. A goodness of fit test is performed to check statistically whether the fitted model provides a good fit with the observed data. We discuss the goodness of fit test based on the Kolmogorov-Smirnov (K-S) test statistic. The proposed model is compared with some of the standard existing models through error sum of squares, mean sum of squares, predictive ratio risk and Akaikes information criteria using three different data sets. We show that the observed data fits the proposed software reliability growth model. We also show that the proposed model performs satisfactory better than the existing finite failure category models

In this paper, we considered a new generalization of the paralogistic distribution which we called the three-parameter paralogistic distribution. Some properties of the new distribution which includes the survival function, hazard function, quantile function, moments, Renyi entropy and the maximum likelihood estimation (MLE) of its parameters are obtained. A simulation study shows that the MLE of the parameters of the new distribution is consistent and asymptotically unbiased. An applicability of the new three-parameter paralogistic distribution was subject to a real lifetime data set alongside with some related existing distributions such as the Paralogistic, Gamma, Transformed Beta, Log-logistic and Inverse paralogistic distributions. The results obtained show that the new three-parameter paralogistic distribution was superior to other aforementioned distributions in terms of the Akaike information criterion (AIC) and K-S Statistic values. This claim was further supported by investigating the density plots, P-P plots and Q-Q plots of the distributions for the data set under study.

The so-called Kumaraswamy distribution is a special probability distribution developed to model doubled bounded random processes for which the mode do not necessarily have to be within the bounds. In this article, a generalization of the Kumaraswamy distribution called the T-Kumaraswamy family is defined using the T-R {Y} family of distributions framework. The resulting T-Kumaraswamy family is obtained using the quantile functions of some standardized distributions. Some general mathematical properties of the new family are studied. Five new generalized Kumaraswamy distributions are proposed using the T-Kumaraswamy method. Real data sets are further used to test the applicability of the new family.

In this paper, we propose a new generalization of exponentiated modified Weibull distribution, called the McDonald exponentiated modified Weibull distribution. The new distribution has a large number of well-known lifetime special sub-models such as the McDonald exponentiated Weibull, beta exponentiated Weibull, exponentiated Weibull, exponentiated expo- nential, linear exponential distribution, generalized Rayleigh, among others. Some structural properties of the new distribution are studied. Moreover, we discuss the method of maximum likelihood for estimating the model parameters.

Abstract: In this paper, we introduce an extended four-parameter Fr´echet model called the exponentiated exponential Fr´echet distribution, which arises from the quantile function of the standard exponential distribution. Various of its mathematical properties are derived including the quantile function, ordinary and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, generating function, Shannon entropy and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new distribution is illustrated by means of three real lifetime data sets. In fact, the new model provides a better fit to these data than the Marshall-Olkin Fr´echet, exponentiated-Fr´echet and Fr´echet models.