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.
In this article, performing and deriving te probability density function for Rayleigh distribution is done by using ordinary least squares estimator method and Rank set estimator method. Then creating interval for scale parameter of Rayleigh distribution. Anew method using is used for fuzzy scale parameter. After that creating the survival and hazard functions for two ranking functions are conducted to show which one is beast.
This paper discusses estimating the two scale parameters of Exponential-Rayleigh distribution for singly type one censored data which is one of the most important Rights censored data, using the maximum likelihood estimation method (MLEM) which is one of the most popular and widely used classic methods, based on an iterative procedure such as the Newton-Raphson to find estimated values for these two scale parameters by using real data for COVID-19 was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. The duration of the study was in the interval 4/5/2020 until 31/8/2020 equivalent to 120 days, where the number of patients who entered the (study) hospital with sample size is (n=785). The number o
... Show MoreThe parameter and system reliability in stress-strength model are estimated in this paper when the system contains several parallel components that have strengths subjects to common stress in case when the stress and strengths follow Generalized Inverse Rayleigh distribution by using different Bayesian estimation methods. Monte Carlo simulation introduced to compare among the proposal methods based on the Mean squared Error criteria.
The stress(Y) – strength(X) model reliability Bayesian estimation which defines life of a component with strength X and stress Y (the component fails if and only if at any time the applied stress is greater than its strength) has been studied, then the reliability; R=P(Y<X), can be considered as a measure of the component performance. In this paper, a Bayesian analysis has been considered for R when the two variables X and Y are independent Weibull random variables with common parameter α in order to study the effect of each of the two different scale parameters β and λ; respectively, using three different [weighted, quadratic and entropy] loss functions under two different prior functions [Gamma and extension of Jeffery
... Show MoreIn this paper, we investigate two stress-strength models (Bounded and Series) in systems reliability based on Generalized Inverse Rayleigh distribution. To obtain some estimates of shrinkage estimators, Bayesian methods under informative and non-informative assumptions are used. For comparison of the presented methods, Monte Carlo simulations based on the Mean squared Error criteria are applied.
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
... Show MoreThis paper demonstrates the construction of a modern generalized Exponential Rayleigh distribution by merging two distributions with a single parameter. The "New generalized Exponential-Rayleigh distribution" specifies joining the Reliability function of exponential pdf with the Reliability function of Rayleigh pdf, and then adding a shape parameter for this distribution. Finally, the mathematical and statistical characteristics of such a distribution are accomplished
In this research, several estimators concerning the estimation are introduced. These estimators are closely related to the hazard function by using one of the nonparametric methods namely the kernel function for censored data type with varying bandwidth and kernel boundary. Two types of bandwidth are used: local bandwidth and global bandwidth. Moreover, four types of boundary kernel are used namely: Rectangle, Epanechnikov, Biquadratic and Triquadratic and the proposed function was employed with all kernel functions. Two different simulation techniques are also used for two experiments to compare these estimators. In most of the cases, the results have proved that the local bandwidth is the best for all the
... Show MoreThis paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a0) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge.
The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about beha
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