Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where      0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta

Weibull Distribution is one of most important distribution and it is mainly used in reliability and in distribution of life time. The study handled two parameter and three-parameter Weibull Distribution in addition to five –parameter Bi-Weibull distribution. The latter being very new and was not mentioned before in many of the previous references. This distribution depends on both the two parameter and the three –parameter Weibull distributions by using the scale parameter (α) and the shape parameter (b) in the first and adding the location parameter (g)to the second and then joining them together to produce a distribution with five parameters.

In this paper a new idea was introduced which is finding a new distribution from other distributions using mixing parameters; w_i  where  0 < w_i < 1 ­and . Therefore we can get many mixture distributions with a number of parameters. In this paper I introduced the idea of a mixture Weibull distribution which is produced from mixing two Weibull distributions; the first with two parameters, the scale parameter , and the shape parameter,  and the second also has the scale parameter , and the shape parameter,  in addition to the location parameter, . These two distributions were mixed using a new parameter which is the mixing parameter w which represents the proportion

Weibull Distribution is one of most important distribution and it is mainly used in reliability and in distribution of life time. The study handled two parameter and three-parameter Weibull Distribution in addition to five –parameter Bi-Weibull distribution. The latter being very new and was not mentioned before in many of the previous references. This distribution depends on both the two parameter and the three –parameter Weibull distributions by using the scale parameter (α) and the shape parameter (b) in the first and adding the location parameter (g)to the second and then joining them together to produce a distribution with five parameters.

In this paper was discussed the process of compounding two distributions using new compounding procedure which is connect a number of life time distributions ( continuous distribution ) where is the number of these distributions represent random variable distributed according to one of the discrete random distributions . Based on this procedure have been compounding zero – truncated poisson distribution with weibell distribution to produce new life time distribution having three parameter , Advantage of that failure rate function having many cases ( increasing , dicreasing , unimodal , bathtube) , and study the resulting distribution properties such as : expectation , variance , comulative function , reliability function and fa

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

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The three parameters distribution called modified weibull distribution (MWD) was introduced first by Sarhan and Zaindin (2009)[1]. In theis paper, we deal with interval estimation to estimate the parameters of modified weibull distribution based on singly type one censored data, using Maximum likelihood method and fisher information to obtain the estimates of the parameters for modified weibull distribution, after that applying this technique to asset of real data which taken for Leukemia disease in the hospital of central child teaching .

        In this paper, estimation of system reliability of the multi-components in stress-strength model R_(s,k) is considered, when the stress and strength are independent random variables and follows the Exponentiated Weibull Distribution (EWD) with known first shape parameter θ and, the second shape parameter α is unknown using different estimation methods. Comparisons among the proposed estimators through  Monte Carlo simulation technique were made depend on mean squared error (MSE)  criteria