In this paper, a Weibull-normal distribution, based on the standard quantile function of log-logistic distribution, is defined and studied. Some properties of the probability distribution are discussed. The Weibull-normal distribution is found to be unimodal or bimodal. The distribution can be right skewed or left skewed. The method of maximum likelihood estimation is suggested to estimate the parameters of the distribution. Three numerical data sets are used to illustrate the applications of the Weibullnormal distribution.

Studies on probability distribution functions and their properties are needful as they are very important in modeling random phenomena. However, research has shown that some real life data can be modeled more adequately by distributions obtained as combination of two random variables with known probability distributions. This paper introduces the Gamma-Rayleigh distribution (GRD) as a new member of the Gamma-X family of generalized distributions. The Transformed-Transformer method is used to combine the Gamma and Rayleigh distributions. Various properties of the resulting twoparameter Gamma-Rayleigh distribution, including moments, moment generating function, survival function and hazard function are derived. Results of simulation study reveals that the distribution is unimodal, skewed and normal-type for some values of the shape parameter. The distribution is also found to relate with the Gamma, Rayleigh and Generalized-Gamma distributions. The method of maximum likelihood has been used to estimate the shape and scale parameters of the distribution. To illustrate its adequacy in modelling real life data the distribution is fitted to two survival data sets. The results show that the distribution produced fits that are competitive and compared better, in some cases, to the Gamma, Rayleigh, Weibull and Lognormal distributions.

Recently, different distributions have been generalized using the T-R {Y} framework but the possibility of using Dagum distribution has not been assessed. The T-R {Y} combines three distributions, with one as a baseline distribution, with the strength of each distribution combined to produce greater effect on the new generated distribution. The new generated distributions would have more parameters but would have high flexibility in handling bimodality in datasets and it is a weighted hazard function of the baseline distribution. This paper therefore generalized the Dagum distribution using the quantile function of Lomax distribution. A member of T-Dagum class of distribution called exponentiated-exponential-Dagum {Lomax} (EEDL) distribution was proposed. The distribution will be useful in survival analysis and reliability studies. Different characterizations of the distribution are derived, such as the asymptotes, stochastic ordering, stress-strength analysis, moment, Shannon entropy, and quantile function. Simulated and real data are used and compared favourably with existing distributions in the literature.

Many existing distributions in literatures does not have the modeling fits capacity to adequately describe the real-life phenomena. The Exponential Pareto (EP) distribution has further gained some generalizations among several authors using different generator techniques with an aim to obtain a new distribution with greater flexibility. This article proposes Gompertz Exponential Pareto (GEP) distribution using the Gompertz generator. Findings from the study revealed some lifetime distributions as special cases and mathematical properties of the distribution investigated including the mean, variance, coefficient of variation, quantile, moment, moment generating function and, order statistics. The distribution can be positively or negatively skewed. It is unimodal with failure rates whose shapes could be reversed J bathtub, constant, decreasing and, increasing and the parameters were estimated using maximum likelihood estimation approach. Applications to two real-life datasets revealed the ability of GEP distribution to provide more flexibilities and better fit to the dataset compared to some previously proposed distributions for the data. The results also revealed that GEP had the superior performance over other generalizations of EP distribution existing in literatures and the performance has further strengthened the usefulness of the Gompertz-generator technique.

In this paper, we compared different Parameter Estimation method of the two parameter Weibull-Rayleigh Distribution (W-RD) namely; Maximum Likelihood Estimation (MLE), Least Square Estimation method (LSE) and three methods of Quartile Estimators. Two of the quartile methods have been applied in literature, while the third method (Q1-M) is introduced in this work. The methods have been applied to simulate data. These methods of estimation were compared using Error, Mean Square Error and Total Deviation (TD) which is also known as Sum Absolute Error Estimate (SAEE). The analytical results show that the performances of all the parameter estimation methods were satisfactory with data set of Weibull-Rayleigh distribution while degree of accuracy is determined by the sample size. The proposed quartile (Q1-M) method has the least Total Deviation and MSE. In addition, the quartile methods perform better than MLE for the simulated data. In particular, the proposed quartile methods (Q1-M) have an added advantage of simplicity in usage than MLE methods.