Inverse Rayleigh Distribution Research Articles

Statistical Inference on Process Capability Index Cpyk for Inverse Rayleigh Distribution under Progressive Censoring

In quality engineering, process capability indexes are used to determine the capability of a process. The well-known of the process capability indexes are Cp, Cpk, Cpm, and Cpmk. These indexes assume the normality of the product lifetime. \citet{maiti2010generalizing} suggested a Cpyk as a generalized process capability index without distributional assumption. In this paper, the maximum likelihood and Bayesian inference on the Cpyk are studied under progressive censoring when the underlying distribution is inverse Rayleigh distribution. Furthermore, Bayesian credible and highest posterior density intervals are discussed with the MCMC procedure. Several types of bootsrap confidence intervals are also considered. A Monte Carlo simulation is conducted in terms of the coverage probabilities and mean lengths of the proposed intervals. An illustrative example is presented to close the paper.
  

Reliability Analysis with New Sine Inverse Rayleigh Distribution

This article examined some of the characteristics of the New Sine Inverse Rayleigh Distribution. There is just one scale parameter in the New Sine Inverse Rayleigh distribution. The raw moments, reliability analysis, and other aspects of the New Sine Inverse Rayleigh Distribution have been derived. The maximum likelihood approach was used to estimate the New Sine Inverse Rayleigh Distribution’s parameters. Utilizing simulation, the distribution’s stability was examined, and the applicability of the distribution was demonstrated using three data sets. The analysis’s findings demonstrated that the New Sine Inverse Rayleigh Distribution behaves well and fits the data more closely than other probability distributions.

Point and Interval Estimation of Stress-Strength Model for Exponentiated Inverse Rayleigh distribution

Point and Interval Estimation of Stress-Strength Model for Exponentiated Inverse Rayleigh distribution

A versatile model for lifetime of a component under stress

In this study, a versatile model, called alpha-monotone inverse Weibull distribution (alphaIW), for lifetime of a component under stress is introduced by using the alpha-monotone concept. The alphaIW distribution is also expressed as a scale-mixture between the inverse Weibull distribution and uniform distribution on (0, 1). The alphaIW distribution includes alpha-monotone inverse exponential and alpha-monotone inverse Rayleigh distributions as submodels and converenges to the inverse Weibull, inverse exponential, and inverse Rayleigh distributions as limiting cases. Also, slash Weibull, slash Rayleigh, and slash exponential distribuitons can be obtained under certain variable transformation and parameter settings. The alphaIW distribution is characterized by its hazard rate function and characterizing conditions are provided as well. Maximum likelihood, maximum product of spacing, and least squares methods are used to estimate distribution parameters. A Monte-Carlo simulation study is conducted to compare the efficiencies of the considered estimation methods. In the application part, two practical data sets, Kevlar 49/epoxy and Kevlar 373/epoxy, are modeled via the alphaIW distribution. Modeling performance of the alphaIW distribution is compared with its rivals by means of some well-known goodness-of-fit statistics and results show that alphaIW distribution performs better modeling than them. Results of comparison also indicate that obtaining the alphaIW distribution by using the alpha-monotone concept is cost effective since the new shape parameter added to the distribution by using the alpha-monotone concept significantly increases the modeling capability of the IW distribution. As a result of this study, it is shown that the alphaIW distribution can be an alternative to the well-known and recently-introduced distributions for modeling purposes.

Powered Inverse Rayleigh Distribution Using DUS Transformation

This article reports an extension of powered inverse Rayleigh distribution via DUS transformation, named DUS-Powered Inverse Rayleigh (DUS-PIR) distribution. Some statistical properties of suggested distribution in particular, moments, mode, quantiles, order statistics, entropy, inequality measures and stress-strength parameter have been investigated extensively. To estimate the parameters, maximum likelihood estimation (MLE) is discussed. The model superiority is verified through two real datasets.

HYBRID DOUBLE EXPONENTIALLY WEIGHTED MOVING AVERAGE (HDEWMA) CONTROL CHART FOR INVERSE RAYLEIGH DISTRIBUTION

In this paper, we proposed a Hybrid Double Exponentially Weighted Moving Average HDEWMA control chart. The proposed control chart is based on Inverse Rayleigh Distributed lifetimes using simple random sampling (SRS) and ranked set sampling (RSS). Out-of-control-Average Run Length (ARL1) is used to evaluate the performance of the proposed control chart. The HDEWMA control chart is compared with traditional/simple EWMA and CUSUM control charts. The performance of the control chart is evaluated using out of control average run length (ARL1). A simulated example is used to compare the proposed HDEWMA, traditional/simple EWMA chart and CUSUM control chart. It is observed that the proposed HDEWMA control chart performs simple EWMA and CUSUM control charts. The HDEWMA control chart can be used for efficient monitoring of the production process in manufacturing industries where the data is coming from inverse Rayleigh Distribution. Keywords: Hybrid, EWMA, CUSUM, DEWMA, average run length (ARL).

Bayesian Methods for Estimation the Parameters of Finite Mixture of Inverse Rayleigh Distribution

Methods 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 Metropolis – Hastings algorithms. The proposed techniques are applied to simulated data following several scenarios. The accuracy of estimation has been examined by the average mean square error (AMSE) and the average classification success rate (ACSR). The results showed that the method was well performed in all simulation scenarios with respect to different sample sizes.

Neutrosophic exponentiated inverse Rayleigh distribution: Properties and Applications

In the field of survival analysis, the exponentiated inverse Rayleigh distribution is used to simulate lifetime data practices of human. In order to describe diverse survival data with indeterminacies, this work aims to create a generalization of the traditional pattern exponentiated inverse Rayleigh distribution, referred to as the neutrosophic exponentiated inverse Rayleigh distribution (NEIRD). In particular, modeling uncertain data that is roughly positively skewed makes use of the established distribution. The key statistical characteristics of the developed NEIRD, such as the neutrosophic survival function, neutrosophic hazard rate and neutrosophic moments, are discussed in this study. Additionally, in a neutrosophic well-known maximum likelihood estimation approach is used to estimate the neutrosophic parameters. A simulation study is conducted to determine whether the estimated neutrosophic parameters were achieved. Last but not least, real data has been used to discuss the potential NEIRD applications in the real world. The effectiveness of the suggested model in comparison to the existing distributions was demonstrated by real data.

Exploring the Exponentiated Transmuted Inverse Rayleigh Distribution (ETIRD) in Classical and Bayesian Paradigms

We derived, a new three parameters continuous probability distribution called Exponentiated Transmuted Inverse Rayleigh Distribution (ETIRD). Various mathematical properties of the new distribution including mean, rth moments, moment generating function, quantile function etc. are derived. In the Classical paradigm, the estimators of the distribution are obtained using the maximum likelihood method. The Bayes estimators are derived under square error loss function (SELF) using non-informative and informative priors via the Lindley approximation technique. Bayes Estimators are compared with their corresponding maximum likelihood Estimators (MLEs) using a Monte Carlo Simulation Study under different sample sizes, different values of true parameters, using informative and non-informative priors. Performance of Bayes estimators and classical estimates is judged for the four real life data sets. The results of simulation study and real-life example show that the Bayes estimators provided better results than MLEs.

MONITORING INVERSE RAYLEIGH DISTRIBUTED LIFETIMES USING DEWMA CONTROL CHART

In this paper, we proposed a Double Exponentially Weighted Moving Average DEWMA control chart. The proposed control chart is based on Inverse Rayleigh Distributed lifetimes using simple random sampling. Out-of-control-Average Run Length (ARL1) is used to evaluate the performance of the proposed control chart. The DEWMA control chart is compared with traditional/simple EWMA and CUSUM control charts. A simulated example is used to compare the proposed DEWMA, traditional/simple EWMA chart control chart. It is observed that the proposed DEWMA control chart performs simple EWMA control charts. The DEWMA control chart can be used for efficient monitoring of the production process in manufacturing industries where the data is coming from inverse Rayleigh Distribution. Keywords: EWMA, CUSUM, DEWMA, average run length (ARL).

Dual generalized order statistics with moments properties using powered inverse Rayleigh distribution

The basic concept of ordered random variables is how the ordering is being done for a model. Dual generalized order statistics (dgos) is one of them. The powered inverse Rayleigh distribution is introduced in this research investigation to analyze the moments’ properties based on dgos. This introduced distribution was coined by Nashaat [1]. The characterization findings based on the recurrence relations and conditional moments are also derived. In addition, some statistical calculations are performed.

Exponential Transformed Inverse Rayleigh Distribution: Statistical Properties and Different Methods of Estimation

In this article a generalization of the inverse Rayleigh distribution has been addressed by using DUS transformation, named as Exponential Transformed Inverse Rayleigh (ETIR) distribution. Some of the statistical properties of this newly proposed distribution like mode, quantiles, moment, moment generating function, survival and hazard rate function have been studied comprehensively. To estimate the parameter of this distribution, four different estimation procedures, such as maximum likelihood estimation (MLE), maximum product spacing method (MPS), least square method (LSE) and weighted least square method (WLSE) are briefly discussed. Performance of these estimates are compared using extensive simulations. As an application point of view the model superiority is verified through two real datasets.

Scheming of reliability sampling plans with some lifetime distributions based on percentiles estimation using intervened Poisson characteristics

In industry, the practice of determining the performance of a product by intervening with the normal working conditions of the manufacturing process is an acceptable method. When reliability is a key quality factor, the reliability single sampling plan is generally used to optimise sample size and estimate time characteristics. The application of Intervened Poisson Distribution (IPD) and some of the lifetime distributions are used in this article to implement a reliability sampling plan. The IPD can be used as a model for counting the defective items in an appropriate situation and the defectiveness will be determined with the help of lifetime distributions. The minimum sample size required to accept a lot and the estimation of the true percentile time of the accepted lots according to the magnitude of the intervention parameter can be found using IPD associated with the Rayleigh Distribution (RD), Exponentiated Rayleigh Distribution (ERD) and Inverse Rayleigh Distribution (IRD). The minimum sample size is necessary to ensure the specified life percentile is obtained under a consumer risk. The operating characteristic (OC) values and estimated percentile time of an accepted lot are presented.

Alpha Power Generalized Inverse Rayleigh Distribution: Its Properties and Applications

This manuscript is related with the development of Alpha Power Generalized Inverse Rayleigh (APGIR) Distribution. The suggested model provides fit of life time data more efficiently. Some of the important characteristics of the suggested model are obtained including moments, moment generating function, quantile, mode, order statistics, stress-strength parameter, and entropies. Parameter estimates are obtained by MLE technique. The performance of the suggested model is evaluated using real-world data sets. The findings of the simulation and real data sets suggest that the newly proposed model is superior to other current competitor models.

Transmuted lower record type inverse rayleigh distribution: estimation, characterizations and applications

This study introduces a new lifetime distribution called the transmuted lower record type inverse Rayleigh which extends the inverse Rayleigh distribution and has the potential to model the recovery times of Covid-19 patients.The new distribution is obtained using the distributions of the first two lower record statistics of the inverse Rayleigh distribution. We discuss some statistical inferences and mathematical properties of the suggested distribution. We examine some characteristics of the proposed distribution such as density shape, hazard function,moments, moment generating function, incomplete moments,Rényi entropy, order statistics, stochastic ordering. We consider five estimation methods such as maximum likelihood, least squares, weighted least squares, Anderson-Darling, Cramér-von Mises for the point estimation of the proposed distribution. Then, a comprehensive Monte Carlo simulation study is carried out to assess the risk behavior of the examined estimators. We provide two real data applications to illustrate the fitting ability of the proposed model, and compare its fit with competitor ones. Unlike many previously proposed distributions, the introduced distribution in this paper has modeled the recovery times of Covid-19 patients.

The Compound Inverse Rayleigh as an Extreme Wind Speed Distribution and Its Bayes Estimation

This paper proposes the Compound Inverse Rayleigh distribution as a proper model for the characterization of the probability distribution of extreme values of wind-speed. This topic is gaining interest in the field of renewable generation, from the viewpoint of assessing both wind power production and wind-tower mechanical reliability and safety. The first part of the paper illustrates such model starting from its origin as a generalization of the Inverse Rayleigh model by means of a continuous mixture generated by a Gamma distribution on the scale parameter, which gives rise to its name. Moreover, its validity for interpreting different field data is illustrated resorting to real wind speed data. Then, a novel Bayes approach for the estimation of such extreme wind-speed model is proposed. The method relies upon the assessment of prior information in a practical way, that should be easily available to system engineers. The results of a large set of numerical simulations—using typical values of wind-speed parameters—are reported to illustrate the efficiency and the accuracy of the proposed method. The validity of the approach is also verified in terms of its robustness with respect to significant differences compared to the assumed prior information.

Does the Type of Records Affect the Estimates of the Parameters?

The maximum likelihood estimation of the unknown parameters of inverse Rayleigh and exponential distributions are discussed based on lower and upper records. The aim is to study the effect of the type of records on the behavior of the corresponding estimators. Mean squared errors are calculated through simulation to study the behavior of the estimators. The results shall be of interest to those situations where the data can be obtained in the form of either of the two types of records and the experimenter must decide between these two for estimation of the unknown parameters of the distribution.

Cubic rank transmuted inverse rayleigh distribution: Properties and applications

Cubic rank transmuted inverse rayleigh distribution: Properties and applications

Statistical Inference of Sine Inverse Rayleigh Distribution

We study in this manuscript a new one-parameter model called sine inverse Rayleigh (SIR) model that is a new extension of the classical inverse Rayleigh model. The sine inverse Rayleigh model is aiming to provide more fitting for real data sets of purposes. The proposed extension is more flexible than the original inverse Rayleigh (IR) model and it hasmany applications in physics and medicine. The sine inverse Rayleigh distribution can havea uni-model and right skewed probability density function (PDF). The hazard rate function (HRF) of sine inverse Rayleigh distribution can be increasing and J-shaped. Several of thenew model’s fundamental characteristics, namely quantile function, moments, incompletemoments, Lorenz and Bonferroni Curves are studied. Four classical estimation methods forthe population parameters, namely least squares (LS), weighted least squares (WLS), maximum likelihood (ML), and percentile (PC) methods are discussed, and the performanceof the four estimators (namely LS, WLS, ML and PC estimators) are also compared bynumerical implementations. Finally, three sets of real data are utilized to compare the behavior of the four employed methods for finding an optimal estimation of the new distribution.

Determination of Hazard State of Non-Communicable Diseases Using Semi-Markov Model

Background: The developed Semi-Markov model with Kumaraswamy Exponentiated Inverse Rayleigh distribution examined patients with hypertension, heart diseases, smoking habits and Stroke, is measured from one state to another. Materials and Methods: Patients with Non-Communicable disease described through Kumaraswamy Exponentiated Inverse Rayleigh distribution. Results: The estimated parameters of Semi-Markov model with this distribution predicted by the maximum likelihood estimation for each successive state observed significant abnormality. The data noted predicts established model is a good fit for many attributes that prevailed in studied data. The developed Semi-Markov model is a best fit for non-Communicable disease in the long run of patient’s data. Through different Exponential family distribution, one can look at for further perfect fit of patient data, which is to be estimated. Conclusion: This model can be an alternative method to estimate the effect of patient in survival analysis, where it will be effective in time consumption in medical field. Keywords: heart diseases, hypertension, Semi-Markov processes, smoking, stroke.