In this research we assumed that the number of emissions by time (𝑡) of radiation particles is distributed poisson distribution with parameter (𝑡), where  < 0 is the intensity of radiation. We conclude that the time of the first emission is distributed exponentially with parameter 𝜃, while the time of the k-th emission (𝑘 = 2,3,4, … . . ) is gamma distributed with parameters (𝑘, 𝜃), we used a real data to show that the Bayes estimator 𝜃 ∗ for 𝜃 is more efficient than 𝜃̂, the maximum likelihood estimator for 𝜃 by using the derived variances of both estimators as a statistical indicator for efficiency

Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem

The Tel Hajar formation in the studied area has been divided into five microfacics units:

1) Fine hiogenic dolomite facies.

2) Sandy rich dolomite facies.

3) Dolomite diagenetic facies.

4) Recrystal1ized wackestone in microfacies.

5) Mudsione facies.

Microfacics reflect shallow marine water with open Circulation in the lower part of the formation and the environment of the upper is enclosed between upper tide and tide. The most important diagenesis was recrystallization and spary calcite deposit inside fossils chambers and pores.

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 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

The present study conducted to study epipelic algae in the Tigris River within Baghdad city for one year from September 2011 to August 2012 due to the importance role of benthic algae in lotic ecosystems. Five sites have been chosen along the river. A total of 154 species of epipelic algae was recorded belongs to 45 genera, where Bacillariophyceae (Diatoms) was the dominant groups followed by Cyanophyceae and Chlorophyceae. The numbers of common types in three sites were 47 species. Bacillariophyceae accounted 88.31% of the total number of epipelic algae, followed by Cyanophyceae 7.14 % and Chlorophyceae 4.55%. A 85 species (29 genera) recorded in site 1, 103 species (34 genera) in site2, 112 species (35 genera) in site3, 96 species

Survival analysis is widely applied to data that described by the length of time until the occurrence of an event under interest such as death or other important events. The purpose of this paper is to use the dynamic methodology which provides a flexible method, especially in the analysis of discrete survival time, to estimate the effect of covariate variables through time in the survival analysis on dialysis patients with kidney failure until death occurs. Where the estimations process is completely based on the Bayes approach by using two estimation methods: the maximum A Posterior (MAP) involved with Iteratively Weighted Kalman Filter Smoothing (IWKFS) and in combination with the Expectation Maximization (EM) algorithm. While the other

The Mishrif Formation is one of the most important geological formations in Iraq consisting of limestone, marl, and shale layers since it is one of the main oil producing reservoirs in the country, which contain a significant portion of Iraq's oil reserves. The formation has been extensively explored and developed by the Iraqi government and international oil companies, with many oil fields being developed within it. The accurate evaluation of the Mishrif formation is key to the successful exploitation of this field. However, its geological complexity poses significant challenges for oil production, requiring advanced techniques to accurately evaluate its petrophysical properties.

   This study used advanced well-logging analysi