In this paper, a new seven-parameter Mittag-Leffler function of a single com-plex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

In this research, the focus was on estimating the parameters on (min- Gumbel distribution), using the maximum likelihood method and the Bayes method. The genetic algorithmmethod was employed in estimating the parameters of the maximum likelihood method as well as  the Bayes method. The comparison was made using the mean error squares (MSE), where the best  estimator  is the one who has the least mean squared error. It was noted that the best estimator was (BLG_GE).

Exponential distribution is one of most common distributions in studies and scientific researches with wide application in the fields of reliability, engineering and in analyzing survival function therefore the researcher has carried on extended studies in the characteristics of this distribution.

In this research, estimation of survival function for truncated exponential distribution in the maximum likelihood  methods and Bayes first and second method, least square method and Jackknife dependent in the first place on the maximum likelihood method, then on Bayes first method then comparing then using simulation, thus to accomplish this task, different size samples have been adopted by the searcher us

In this research, the focus was placed on estimating the parameters of the Hypoexponential distribution function using the maximum likelihood method and genetic algorithm. More than one standard, including MSE, has been adopted for comparison by Using the simulation method

      In this study, different methods were used for estimating location parameter  and scale parameter for extreme value distribution, such as maximum likelihood estimation (MLE) , method of moment  estimation (ME),and approximation  estimators based on percentiles which is called white method in estimation, as the extreme value distribution is one of exponential distributions. Least squares estimation (OLS) was used, weighted least squares estimation (WLS), ridge regression estimation (Rig), and adjusted ridge regression estimation (ARig) were used. Two parameters for expected value to the percentile  as estimation for distribution f

In this research is estimated the function of reliability dynamic of multi state systems  and their compounds and for three types of systems (serial, parallel, 2-out-of-3) and about two states (Failure and repair) depending on calculating the structur function allow to describing the behavior of

Each phenomenon contains several variables. Studying these variables, we find mathematical formula to get the joint distribution and the copula that are a useful and good tool to find the amount of correlation, where the survival function was used to measure the relationship of age with the level of cretonne in the remaining blood of the person. The Spss program was also used to extract the influencing variables from a group of variables using factor analysis and then using the Clayton copula function that is used to find the shared binary distributions using multivariate distributions, where the bivariate distribution was calculated, and then the survival function value was calculated for a sample size (50) drawn from Yarmouk Ho

The two parameters of Exponential-Rayleigh distribution were estimated using the maximum likelihood estimation method (MLE) for progressively censoring data. To find estimated values for these two scale parameters using real data for COVID-19 which was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. Then the Chi-square test was utilized to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). Employing the nonlinear membership function (s-function) to find fuzzy numbers for these parameters estimators. Then utilizing the ranking function transforms the fuzzy numbers into crisp numbers. Finally, using mean square error (MSE) to compare the outcomes of the survival

In this paper, point estimation for parameter ? of Maxwell-Boltzmann distribution has been investigated by using simulation technique, to estimate the parameter by two sections methods; the first section includes Non-Bayesian estimation methods, such as (Maximum Likelihood estimator method, and Moment estimator method), while the second section includes standard Bayesian estimation method, using two different priors (Inverse Chi-Square and Jeffrey) such as (standard Bayes estimator, and Bayes estimator based on Jeffrey's prior). Comparisons among these methods were made by employing mean square error measure. Simulation technique for different sample sizes has been used to compare between these methods.