Journal of Data Science

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 introduce some new families of generalized Pareto distributions using the T-R{Y} framework. These families of distributions are named T-Pareto{Y} families, and they arise from the quantile functions of exponential, log-logistic, logistic, extreme value, Cauchy and Weibull distributions. The shapes of these T-Pareto families can be unimodal or bimodal, skewed to the left or skewed to the right with heavy tail. Some general properties of the T-Pareto{Y} family are investigated and these include the moments, modes, mean deviations from the mean and from the median, and Shannon entropy. Several new generalized Pareto distributions are also discussed. Four real data sets from engineering, biomedical and social science are analyzed to demonstrate the flexibility and usefulness of the T-Pareto{Y} families of distributions.

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.

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.

The Pareto distribution is a power law probability distribution that is used to describe social scientific, geophysical, actuarial, and many other types of observable phenomena. A new weighted Pareto distribution is proposed using a logarithmic weight function. Several statistical properties of the weighted Pareto distribution are studied and derived including cumulative distribution function, location measures such as mode, median and mean, reliability measures such as reliability function, hazard and reversed hazard functions and the mean residual life, moments, shape indices such as skewness and kurtosis coefficients and order statistics. A parametric estimation is performed to obtain estimators for the distribution parameters using three different estimation methods the maximum likelihood method, the L-moments method and the method of moments. Numerical simulation is carried out to validate the robustness of the proposed distribution. The distribution is fitted to a real data set to show its importance in real life applications.