This study includes the application of non-parametric methods in estimating the conditional survival function of the Beran method using both the Nadaraya-Waston and the Priestley-chao weights and using data for Interval censored and Right censored of breast cancer and two types of treatment, Chemotherapy and radiation therapy Considering age is continuous variable, through using (MATLAB)  use of the (MSE) To compare weights The results showed a superior weight (Nadaraya-Waston) in estimating the survival function and condition of Both for chemotherapy and radiation therapy.

     This paper is concerned with preliminary test double stage shrinkage estimators to estimate the variance (s²) of normal distribution when a prior estimate  of the actual value (s²) is a available when the mean is unknown  , using specifying shrinkage weight factors y(×) in addition to pre-test region (R).

      Expressions for the Bias, Mean squared error [MSE (×)], Relative Efficiency [R.EFF (×)], Expected sample size [E(n/s²)] and percentage of overall sample saved of proposed estimator were derived. Numerical results (using MathCAD program) and conclusions are drawn about selection of different constants including in the me

In this paper, the Azzallini’s method used to find a weighted distribution derived from the standard Pareto distribution of type I (SPDTI) by inserting the shape parameter (θ) resulting from the above method to cover the period (0, 1] which was neglected by the standard distribution. Thus, the proposed distribution is a modification to the Pareto distribution of the first type, where the probability of the random variable lies within the period  The properties of the modified weighted Pareto distribution of the type I (MWPDTI) as the probability density function ,cumulative distribution function, Reliability function , Moment and  the hazard function are found. The behaviour of probability density function for MWPDTI distrib

In this paper, we proposed a new class of weighted Rayleigh distribution based on two parameters, scale and shape parameters which are introduced in Rayleigh distribution. The main properties of this class are investigated and derived.

Beta Distribution

Abstract

             Gamma and Beta Distributions has very important in practice in various areas of statistical and applications reliability and quality control of production. and There are a number of methods to generate data behave on according to these distribution. and These methods bassic primarily on the shape parameters of each distribution and the relationship between these distributions and their relationship with some other probability distributions.    &nb

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the <

In this paper, the construction of Hermite wavelets functions and their operational matrix of integration is presented. The Hermite wavelets method is applied to solve nth order Volterra integro diferential equations (VIDE) by expanding the unknown functions, as series in terms of Hermite wavelets with unknown coefficients. Finally, two examples are given

The effect of different antibiotics on growth pigment and plasmid curing of Serratia marcescens were studied, S. marcescens was cultured in media containing(16_500)µg/ml of antibiotics, curing mutants unable to produce prodigiosin and lost one plasmid band were obtained of of ampicillin, amoxillin, antibiotics concentrations (64 500) µg/ml metheprim, ultracloxam, azithromycin, cephalexin and erythromycin treated with (350 500) µg/ml of The mutant cells rose- light color and and refampicin revealed S.marcescens inhibited ciprodar and tetracyclin, lincomycin did not lost the plasmid band chlaforan

In this paper, the Decomposition method was used to find approximation solutions for a system of linear Fredholm integral equations of the second kind. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution, and Adomian decomposition method for solving linear and nonlinear integral equations. Finally, numerical examples are prepared to illustrate these considerations.

Longitudinal data is becoming increasingly common, especially in the medical and economic fields, and various methods have been analyzed and developed to analyze this type of data.

In this research, the focus was on compiling and analyzing this data, as cluster analysis plays an important role in identifying and grouping co-expressed subfiles over time and employing them on the nonparametric smoothing cubic B-spline model, which is characterized by providing continuous first and second derivatives, resulting in a smoother curve with fewer abrupt changes in slope. It is also more flexible and can pick up on more complex patterns and fluctuations in the data.

The longitudinal balanced data profile was compiled into subgroup