This article proposes a class of generator for classical statistical distribution called the shifted Gompertz-G (SHIGO-G) distribution for generating new continuous distributions. Special models of the proposed model were examined together with some of its statistical properties in closed form which makes it tractable for censored data. Its major properties include heavy tail, approximately symmetric, left and right skewed with a combination of exponential and a reverted Gumbel distributions called the Gompertz. The bivariate SHIGO-G is introduced. The parameters estimate of the proposed model was obtained by maximum likelihood method. A Monte Carlo simulation study was employed to investigate the performance of the estimators of the proposed model mean, variance, bias and mean square error. A two real life illustration was used to examine the empirical goodness-of-fit of the test statistic of the proposed model. The results of the real life applications show that the SHIGO-G model provides a better fit for the data set used.

This article proposes a new class of models called the transmuted alpha power-G (TAPO-G) family of distribution for modeling lifetime processes. This class of model extends the well-known existing transmuted distributions. A comprehensive statistical structural property of the proposed model is established. The parameters of the proposed model are obtained by maximum likelihood method. The performance of the TAPO-G maximum likelihood estimators was accessed by the means, variance, mean squared errors and biases of the Monte Carlo simulation study. The proposed model usefulness was examined by real life data illustrations. The new family of distribution proposed provides a better fit when compared with other existing models and can serve as an alternative model in literature.

This article introduces a new generator called the shifted exponential-G (SHE-G) generator for generating continuous distributions. The proposed model extends the existing shifted exponential and the exponential family of distributions. Some special models of the proposed model are presented. The density, hazard rate function and survival rate function of the SHE-G distribution are investigated and examined. The parameters of the SHE-G distribution are obtained by maximum likelihood method. The Bernstein method of generating the SHE-G model was also examined. A two bivariate approach for the proposed model was considered. A simulation was used to examine the performance of the estimators. A three real life data was employed to examine the goodness-of-fit test statistics of the empirical flexibility. The results of the test statistics show that the SHE-G distribution provides a better goodness-of-fit.

This study introduces a parsimonious and tractable generator for continuous distribution called the Teissier-G family of distributions for continuous random variables and examines the distributions belonging to this family as the sub-models. Some general statistical characteristics and sub-models of the new generator were examined and studied. Similarly, we examined the shapes of the sub-models probability density function (pdf) and hazard rate function were investigated. The parameter of the proposed model was obtained in a closed form by maximum likelihood. In addition to the numerical real life applications, Monte Carlo simulation was performed to examine the flexibility of the introduced models. The models provide good fits in all the cases. The results show great improvement compared to existing models.

This article proposed a Weibull-Alpha Power Inverted Exponential (WAPIE) distribution for lifetime processes. Statistical properties of this distribution such as survival, hazard, reversed hazard, cumulative, odd functions, kurtosis, quantiles, skewness, order statistics and the entropies were derived. Parameters of this family of distribution were also obtained by maximum likelihood method. The behaviour of the estimators was studied through simulation. The behavior of the new developed distribution was further examined through real life data. The WAPIE distribution competes favourably well with other distributions.