A new one-parameter discrete distribution, namely discrete Burr-Hatke distribution is introduced and its mathematical properties are studied comprehensively. The main properties of the discrete Burr-Hatke distribution such as mean, variance, skewness and kurtosis measures are obtained in explicit forms. Several parameter estimation methods are used to obtain unknown model parameters and these estimation methods are compared via simulation study. The discrete Burr-Hatke distribution is over-dispersed since its variance is greater than its mean. This property of the proposed distribution opens a new opportunity to model over-dispersed data sets. To show the importance of the proposed distribution against the existing discrete probability distributions, three data sets in different fields are analyzed. Additionally, count regression model based on the discrete Burr-Hatke distribution is introduced with its residual analysis.

In this paper, we introduce a new two-parameter distribution, called log-weighted exponential (log-WE) distribution, defined on the unit interval. Some of the statistical properties of the proposed distribution including moments, incomplete moments and mean residual life function are obtained. The maximum likelihood, method of moments, least squares and weighted least squares estimation methods are used to estimate unknown parameters of the proposed model and finite sample performance of estimation methods are evaluated through Monte-Carlo simulation study. Moreover, a new regression model as an alternative to the beta regression model is introduced.

In this study, we introduce a new family of continuous distributions with one extra shape parameter, called the Burr-Hatke-G family, based on the Burr-Hatke differential equation. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. Moreover, the log-Burr-Hatke-Weibull regression model based on new the generated family is introduced. The usefulness of the proposed family is demonstrated by means of the three real data applications. Empirical results indicate that the proposed family provides more realistic fits than other well-known family of distributions.

A New Extended G Family of Continuous Distributions with Mathematical Properties, Characterizations and Regression Modeling

In this study, a new two-parameter mixed-Poisson distribution is proposed. Statistical properties of the proposed distribution are studied comprehensively. The maximum likelihood estimation method is used to estimate unknown model parameters. A simulation study is conducted to evaluate the asymptotic efficiencies of the maximum likelihood estimators of model parameters. The usefulness of proposed distribution is demonstrated in first-order integer-valued autoregressive process, shortly INAR(1). Empirical findings show that the proposed INAR(1) process provides better results than other competitive models when the time series of counts display over-dispersion.