This paper concerns with the estimation of parameters for the Exponentiated Lomax Distribution ELD.Different estimation methods such as maximum likelihood, quasi-likelihood, Bayesian and quasi-Bayesian are used to evaluate parameters. Numerical study is discussed to illustrate the optimal procedure using MATHCAD program (2001). A comparison between the four estimation methods will be performed.

In this paper, a composite distribution of Kumaraswamy and Lindley distributions namely, Kumaraswamy-Lindley Kum-L distribution is introduced and studied. The Kum-L distribution generalizes sub-models for some widely known distributions. Some mathematical properties of the Kum-L such as hazard function, quantile function, moments, moment generating function and order statistics are obtained. Estimation of parameters for the Kum-L using maximum likelihood estimation and least square estimation techniques are provided. To illustrate the usefulness of the proposed distribution, simulation study and real data example are used.

In this paper, we establish some recurrence relations satisfied by single and product moments of k-th upper record values from the flexible Weibull distribution. We also give a characterization of flexible Weibull distribution by using the recurrence relations for single moments.

In this paper, a new distribution namely, The Marshall–OlkinGeneralized Inverse Weibull Distribution is illustrated and studied. The new distribution is very flexible and contains sub-models such asinverse exponential, inverse Rayleigh, Weibull, inverse Weibull, Marshall–Olkininverse Weibull and Fréchetdistributions. Also, the hazard function of the new distribution can produce variety of forms:an increase, a decrease and an upside-down bathtub. Some properties such as hazard function, quintile function, entropy, moment generating function and order statistics are obtained. Different estimation approaches namely, maximum likelihood estimators, interval estimators, least square estimators, fisher information matrix and asymptotic confidence intervals are described. To illustrate the superior performance of the proposed distribution, a simulation study and a real data analysis are investigated against other models.

This paper considers life-testing experiments and how it is effected by stress factors: namely temperature, electricity loads, cycling rate and pressure. A major type of accelerated life tests is a step-stress model that allows the experimenter to increase stress levels more than normal use during the experiment to see the failure items. The test items are assumed to follow Gamma Dual Weibull distribution. Different methods for estimating the parameters are discussed. These include Maximum Likelihood Estimations and Confidence Interval Estimations which is based on asymptotic normality generate narrow intervals to the unknown distribution parameters with high probability. MathCAD (2001) program is used to illustrate the optimal time procedure through numerical examples.