No abstract

A new class of distributions called the log-logistic Weibull-Poisson distribution is introduced and its properties are explored. This new distribution represents a more flexible model for lifetime data. Some statistical properties of the proposed distribution including the expansion of the density function, quantile function, hazard and reverse hazard functions, moments, conditional moments, moment generating function, skewness and kurtosis are presented. Mean deviations, Bonferroni and Lorenz curves, Rényi entropy and distribution of the order statistics are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the confidence interval for each parameter and finally applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.

No abstract

The assumption that is usually made when modeling count data is that the response variable, which is the count, is correctly reported. Some counts might be over-or under-reported. We derive the Generalized Poisson-Poisson mixture regression (GPPMR) model that can handle accurate, underreported and overreported counts. The parameters in the model will be estimated via the maximum likelihood method. We apply the GPPMR model to a real-life data set.

No abstract