The question of estimation took a great interest in some engineering, statistical applications, various applied, human sciences, the methods provided by it helped to identify and accurately the many random processes.

In this paper, methods were used through which the reliability function, risk function, and estimation of the distribution parameters were used, and the methods are (Moment Method, Maximum Likelihood Method), where an experimental study was conducted using a simulation method for the purpose of comparing the methods to show which of these methods are competent in practical application This is based on the observations generated from the Rayleigh logarithmic distribution (RL) with sample sizes

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.

Abstract

In this research provide theoretical aspects of one of the most important statistical distributions which it is Lomax, which has many applications in several areas, set of estimation methods was used(MLE,LSE,GWPM) and compare with (RRE) estimation method ,in order to find out best estimation method set of simulation experiment (36) with many replications  in order  to get mean square error and used it to make compare , simulation experiment  contrast with (estimation method, sample size ,value of location and shape parameter) results show that estimation method effected by simulation experiment factors and ability of using other estimation methods such as(Shrinkage, jackknif

The Log-Logistic distribution is one of the important statistical distributions as it can be applied in many fields and biological experiments and other experiments, and its importance comes from the importance of determining the survival function of those experiments. The research will be summarized in making a comparison between the method of maximum likelihood and the method of least squares and the method of weighted least squares to estimate the parameters and survival function of the log-logistic distribution using the comparison criteria MSE, MAPE, IMSE, and this research was applied to real data for breast cancer patients. The results showed that the method of Maximum likelihood best in the case of estimating the paramete

This paper deals with defining Burr-XII, and how to obtain its p.d.f., and CDF, since this distribution is one of failure distribution which is compound distribution from two failure models which are Gamma model and weibull model. Some equipment may have many important parts and the probability distributions representing which may be of different types, so found that Burr by its different compound formulas is the best model to be studied, and estimated its parameter to compute the mean time to failure rate. Here Burr-XII rather than other models is consider  because it is used to model a wide variety of phenomena including crop prices, household income, option market price distributions, risk and travel time. It has two shape-parame

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

In this paper, we will illustrate a gamma regression model assuming that the dependent variable (Y) is a gamma distribution and that it's mean ( ) is related through a linear predictor with link function which is identity link function g(μ) = μ. It also contains the shape parameter which is not constant and depends on the linear predictor and with link function which is the log link and we will estimate the parameters of gamma regression by using two estimation methods which are The Maximum Likelihood and the Bayesian and a comparison between these methods by using the standard comparison of average squares of error (MSE), where the two methods were applied to real da

     We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD)

The estimation of the parameters of Two Parameters Gamma Distribution in case of missing data has been made by using two important methods: the Maximum Likelihood Method and the Shrinkage Method. The former one consists of three methods to solve the MLE non-linear equation by which the estimators of the maximum likelihood can be obtained: Newton-Raphson, Thom and Sinha methods. Thom and Sinha methods are developed by the researcher to be suitable in case of missing data. Furthermore, the Bowman, Shenton and Lam Method, which depends on the Three Parameters Gamma Distribution to get the maximum likelihood estimators, has been developed. A comparison has been made between the methods in the experimental aspect to find the best meth