Background In general, truncated distributions provide a flexible framework that allows for more realistic and accurate representation of constrained data compared to using non-truncated distributions, making them a fundamental element in modern statistical models and the analysis of constrained data. Methods Right – truncated [0,1] exponential Rayleigh distribution ([0,1]-RTERD) for lifetime is presented in this paper. The new distribution contains two parameters, one of scale and another for the shape. Statistical functions of the (RTERD), such as cumulative functions (CDF), probability density (PDF), survival, and hazard functions, are presented in terms of mathematical construction and graphics. Besides, discuss the mathematical and statistical properties of the new distribution, including median, moments of the origin, coefficients of skewness and kurtosis, order statistic, moment generating function, the rėnyi entropy, quantile function. Results the parameters of this life expectancy distribution will be estimate using the maximum likelihood estimation method and compare new continuous model with other continuous distributions using statistical information criterion. Finally, apply the ([0,1]-RTERD) to actual datasets to validate the model’s practicality. The ([0,1]-RTERD) frequently produces a better fit and shows more modeling precision when handling lifespan and reliability data, according to comparisons with traditional models. Conclusions The [0,1]-RTERD provides a new framework for more accurately dealing with data restricted to the interval [0,1], where it is characterized by several important properties, including changing the shape, center, and width of the original distribution as a result of the normalization process, which is reflected in the expected value, standard deviation, and other instantaneous properties.
This paper aims to deal with the understanding of the properties of the molecular gas hydrogen in the extragalactic spirals sample. It is critical to make observations of CO (J = 1-0) line emission for spiral galaxies, particularly those with an energetic nucleus. In the sample of spiral galaxies compiled, a carbon monoxide CO (1-0) emission line can be observed. This sample of galaxies' gas kinematics and star-forming should be analyzed statistically utilizing appropriate atomic gas HI, molecular gas H2, infrared (1μm-1000μm), visual (at λblue-optical=4400A0), and radio spectrum (at νradio=1.4 GHz and 5GHz) databases. STATISTICA is software that allows us to perform this statistical analysis. The presence of a high scale of s
... Show MoreStatistical methods and statistical decisions making were used to arrange and analyze the primary data to get norms which are used with Geographic Information Systems (GIS) and spatial analysis programs to identify the animals production and poultry units in strategic nutrition channels, also the priorities of food insecurity through the local production and import when there is no capacity for production. The poultry production is one of the most important commodities that satisfy human body protein requirements, also the most important criteria to measure the development and prosperity of nations. The poultry fields of Babylon Governorate are located in Abi Ghareg and Al_Kifil centers according to many criteria or factors such as the popu
... Show MoreThe research presents the reliability. It is defined as the probability of accomplishing any part of the system within a specified time and under the same circumstances. On the theoretical side, the reliability, the reliability function, and the cumulative function of failure are studied within the one-parameter Raleigh distribution. This research aims to discover many factors that are missed the reliability evaluation which causes constant interruptions of the machines in addition to the problems of data. The problem of the research is that there are many methods for estimating the reliability function but no one has suitable qualifications for most of these methods in the data such
The Estimation Of The Reliability Function Depends On The Accuracy Of The Data Used To Estimate The Parameters Of The Probability distribution, and Because Some Data Suffer from a Skew in their Data to Estimate the Parameters and Calculate the Reliability Function in light of the Presence of Some Skew in the Data, there must be a Distribution that has flexibility in dealing with that Data. As in the data of Diyala Company for Electrical Industries, as it was observed that there was a positive twisting in the data collected from the Power and Machinery Department, which required distribution that deals with those data and searches for methods that accommodate this problem and lead to accurate estimates of the reliability function,
... Show MoreThis paper delves into some significant performance measures (PMs) of a bulk arrival queueing system with constant batch size b, according to arrival rates and service rates being fuzzy parameters. The bulk arrival queuing system deals with observation arrival into the queuing system as a constant group size before allowing individual customers entering to the service. This leads to obtaining a new tool with the aid of generating function methods. The corresponding traditional bulk queueing system model is more convenient under an uncertain environment. The α-cut approach is applied with the conventional Zadeh's extension principle (ZEP) to transform the triangular membership functions (Mem. Fs) fuzzy queues into a family of conventional b
... Show MoreThis 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.
A comparison of double informative and non- informative priors assumed for the parameter of Rayleigh distribution is considered. Three different sets of double priors are included, for a single unknown parameter of Rayleigh distribution. We have assumed three double priors: the square root inverted gamma (SRIG) - the natural conjugate family of priors distribution, the square root inverted gamma – the non-informative distribution, and the natural conjugate family of priors - the non-informative distribution as double priors .The data is generating form three cases from Rayleigh distribution for different samples sizes (small, medium, and large). And Bayes estimators for the parameter is derived under a squared erro
... Show MoreMethods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and
... Show MoreStrong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.