Journal of Data Science

Many software reliability growth models based upon a non-homogeneous Poisson process (NHPP) have been proposed to measure and asses the reliability of a software system quantitatively. Generally, the error detection rate and the fault content function during software testing is considered to be dependent on the elapsed time testing. In this paper we have proposed three software reliability growth models (SRGM’s) incorporating the notion of error generation over the time as an extension of the delayed S-shaped software reliability growth model based on a non-homogeneous Poisson process (NHPP). The model parameters are estimated using the maximum likelihood method for interval domain data and three data sets are provided to illustrate the estimation technique. The proposed model is compared with the existing delayed S-shaped model based on error sum of squares, mean sum of squares, predictive ratio risk and Akaike’s information criteria using three different data sets. We show that the proposed models perform satisfactory better than the existing 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.