By driven the moment estimator of ARMA (1, 1) and by using the simulation some important notice are founded, From the more notice conclusions that the relation between the sign   and moment estimator for ARMA (1, 1) model that is: when the sign is positive means the root      gives invertible model and when the sign is negative means the root      gives invertible model. An alternative method has been suggested for ARMA (0, 1) model can be suitable when

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

The analysis of survival and reliability considered of topics and methods of vital statistics at the present time because of their importance in the various demographical, medical, industrial and engineering fields. This research focused generate random data for samples from the probability distribution Generalized Gamma: GG, known as: "Inverse Transformation" Method: ITM, which includes the distribution cycle integration function incomplete Gamma integration making it more difficult classical estimation so will be the need to illustration to the method of numerical approximation and then appreciation of the function of survival function. It was estimated survival function by simulation the way "Monte Carlo". The Entropy method used for the

المستخلص:

          في هذا البحث , استعملنا طرائق مختلفة لتقدير معلمة القياس للتوزيع الاسي كمقدر الإمكان الأعظم ومقدر العزوم ومقدر بيز في ستة أنواع مختلفة عندما يكون التوزيع الأولي لمعلمة القياس : توزيع لافي  (Levy) وتوزيع كامبل من النوع الثاني وتوزيع معكوس مربع كاي وتوزيع معكوس كاما وتوزيع غير الملائم (Improper) وتوزيع

The statistical distributions study aimed to obtain on best descriptions  of variable sets phenomena, which each of them got one behavior of that distributions .  The estimation operations study for that distributions considered of important things which could n't canceled in variable behavior study, as result  this research came as trial for reaching to best method for information distribution estimation which is generalized linear failure rate distribution, throughout studying the theoretical sides by depending on statistical posteriori methods  like greatest ability, minimum squares method and Mixing method (suggested method).        

The research

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimati

Abstract

The research Compared two methods for estimating fourparametersof the compound exponential Weibull - Poisson distribution which are the maximum likelihood method and the Downhill Simplex algorithm. Depending on two data cases, the first one assumed the original data (Non-polluting), while the second one assumeddata contamination. Simulation experimentswere conducted for different sample sizes and initial values of parameters and under different levels of contamination. Downhill Simplex algorithm was found to be the best method for in the estimation of the parameters, the probability function and the reliability function of the compound distribution in cases of natural and contaminateddata.

لاهمية التوزيع المختلط في التعبيرعن التوزيعات الاحتمالية للمتغيرات العشوائية المختلطة من النوعين المتقطع والمستمر ، حيث انها تاخذ قيم أحتمالية موجبة عن نقاط معرفة لقيم x

وتاخذ دالة او قيم اخرى عندما تقع    x ضمن مجال معين                            .(Interval)

وحاول

Transforming the common normal distribution through the generated Kummer Beta model to the Kummer Beta Generalized Normal Distribution (KBGND) had been achieved. Then, estimating the distribution parameters and hazard function using the MLE method, and improving these estimations by employing the genetic algorithm. Simulation is used by assuming a number of models and different sample sizes. The main finding was that the common maximum likelihood (MLE) method is the best in estimating the parameters of the Kummer Beta Generalized Normal Distribution (KBGND) compared to the common maximum likelihood according to Mean Squares Error (MSE) and Mean squares Error Integral (IMSE) criteria in estimating the hazard function. While the pr