Inverse Rayleigh Distribution Research Articles

Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution

Abstract A three-parameter continuous distribution is constructed, using a power transformation related to the transmuted inverse Rayleigh (TIR) distribution. A comprehensive account of the statistical properties is provided, including the following: the quantile function, moments, incomplete moments, mean residual life function and Rényi entropy. Three classical procedures for estimating population parameters are analysed. A simulation study is provided to compare the performance of different estimates. Finally, a real data application is used to illustrate the usefulness of the recommended distribution in modelling real data.

Estimation of multicomponent stress-strength reliability from exponentiated inverse Rayleigh distribution

This paper deals with the classical and Bayesian estimation of multicomponent stress-strength reliability through assuming the exponentiated inverse Rayleigh distribution. Assuming that both stress and strength variates are follows to exponentiated inverse Rayleigh distribution with common and known shape parameter. The multicomponent stress-strength reliability of a system is obtained by the methods of maximum likelihood and Bayesian approach. The results are compared using Markov Chain Monte Carlo (MCMC) technique for both small and large samples. Finally, two data sets of coating weights of iron sheets are analyzed for illustrative purposes.

Design of X-bar control chart based on Inverse Rayleigh Distribution under repetitive group sampling

The X¯ control chart is usually used in statistical quality control (SQC) to observe the change in procedure mean. In this paper, X¯ control chart for Inverse Rayleigh Distribution (IRD) is designed under repetitive group sampling at lower record values. The width of the X¯ control limits and power is established by using the mean and standard deviation of the Inverse Rayleigh Distribution based upon lower record values. The designed control chart’s Average Run Length (ARL) is determined for different values of the shift, sample size, lower record, and specified ARL. The already existed X¯ control chart is used for the comparison and to propose a new X¯ control chart for Inverse Rayleigh Distribution.

On Bayesian Estimation of System Reliability in Stress – Strength Model Based on Generalized Inverse Rayleigh Distribution

The 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.

Pivotal Inference for the Inverted Exponentiated Rayleigh Distribution Based on Progressive Type-II Censored Data

In this article, the pivotal inference is proposed to estimate the two unknown parameters of the inverse exponentiated Rayleigh distribution based on progressive censored data. We derive the point estimator and construct an interval estimator using the pivotal quantity method. To compare the performance of this proposed method and the traditional maximum likelihood estimation method, a simulation study is conducted. The simulation results show that the proposed method performs better in terms of bias and mean squared error. Finally, a real dataset is used to illustrate the proposed approaches.

Bayesian Estimators of the parameter and Reliability Function of Inverse Rayleigh Distribution" A comparison study "

In this paper, Bayesian estimator for the parameter and reliability function of inverse Rayleigh distribution (IRD) were obtained Under three types of loss function, namely, square error loss function (SELF), Modified Square error loss function (MSELF) and Precautionary loss function (PLF),taking into consideration the informative and non- informative prior. The performance of such estimators was assessed on the basis of mean square error (MSE) criterion by performing a Monte Carlo simulation technique.

Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution.

The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models.

ENTROPY-BASED AND NON-ENTROPY-BASED GOODNESS OF FIT TEST FOR THE INVERSE RAYLEIGH DISTRIBUTION WITH PROGRESSIVELY TYPE-II CENSORED DATA

In this paper, the problem of goodness of fit test for the inverse Rayleigh distribution based on progressively Type-II censored samples is studied. We develop two test statistics via entropy and propose one new non-entropy test statistic via a pivotal method. We also study the properties of these test statistics. Critical values are obtained by simulations. Then, we do power analysis of these test statistics against various alternatives under different censoring schemes. We conclude that the tests we proposed perform well against various alternatives, especially for non-monotone hazard alternatives. Finally, one real data set is analyzed.

A Univariate, Bivariate and Multivariate Extensions for the Inverse Rayleigh Model with Properties and Applications to the Univariate Version

A new univariate extension of the Inverse Rayleigh distribution is proposed and studied. Some of its fundamental statistical properties such as some stochastic properties, ordinary and incomplete moments, moments generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering, Rényi, Shannon and q-entropies are derived. A simple type Copula based construction via Morgenstern family and via Claytoncopula is employed to derive many bivariate and multivariate extensions of the new model. We assessed the performance of the maximum likelihood estimators using a simulation study. The importance of the new model is shown via two applications to real data sets.

THE NEW WEIGHTED INVERSE RAYLEIGH DISTRIBUTION AND ITS APPLICATION

In this study, a new weighted version of the inverse Rayleigh distribution based on two different weight functions is introduced. Some statistical and reliability properties of the introduced distribution including the moments, moment generating function, entropy measures (i.e., Shannon and R´enyi) and survival and hazard rate functions are derived. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms. So, a numerical method has been required to compute maximum likelihood estimates. Finally, the daily mean wind speed data set has been analysed to show the usability of the new weighted inverse Rayleigh distribution.

Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test

ABSTRACT In this work, we propose a new three parameter distribution called the Burr XII inverse Rayleigh model, this model is a generalization of the inverse Rayleigh distribution using the Burr XII family introduced by Cordeiro et al. [The burr XII system of densities: properties, regression model and applications. J. Stat. Comput. Simul. 88 (2018), pp. 432–456]. After studying the statistical characterization of this model, we construct a modified chi-squared goodness-of-fit test based on the Nikulin–Rao–Robson statistic in the presence of two cases: censored and complete data. We describe the theory and the mechanism of the statistic test which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on initial non grouped data. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various fields, we illustrate it and the proposed test by applications to two real data sets for complete data case and two other data sets in the presence of right censored.

Transmuted Alpha Power Inverse Rayleigh Distribution: Properties and Application

This paper proposes a new three parameter-distribution through the technique known as Transmutation. The proposed distribution is named Transmuted Alpha power inverse Rayleigh Distribution. Several important properties of the distribution are derived. The parameter estimation is also carried out. Two real life data set are used at the end to describe the potential application of proposed model.

Exponentiated Inverse Rayleigh Distribution and an Application to Coating Weights of Iron Sheets Data

This article aims to introduce a generalization of the inverse Rayleigh distribution known as exponentiated inverse Rayleigh distribution (EIRD) which extends a more flexible distribution for modeling life data. Some statistical properties of the EIRD are investigated, such as mode, quantiles, moments, reliability, and hazard function. We describe different methods of parametric estimations of EIRD discussed by using maximum likelihood estimators, percentile based estimators, least squares estimators, and weighted least squares estimators and compare those estimates using extensive numerical simulations. The performances of the proposed methods of estimation are compared by Monte Carlo simulations for both small and large samples. To illustrate these methods in a practical application, a data analysis of real-world coating weights of iron sheets is obtained from the ALAF industry, Tanzania, during January-March, 2018. ALAF industry uses aluminum-zinc galvanization technology in the coating process. This application identifies the EIRD as a better model than other well-known distributions in modeling lifetime data.

Estimation of Stress–Strength Reliability from Exponentiated Inverse Rayleigh Distribution

This paper considers the estimation of stress–strength reliability when two independent exponential inverse Rayleigh distributions with different shape parameters and common scale parameter. The maximum likelihood estimator (MLE) of the reliability, its asymptotic distribution and asymptotic confidence intervals are constructed. Comparisons of the performance of the estimators are carried out using Monte Carlo simulations, the mean squared error (MSE), bias, average length and coverage probabilities. Finally, a demonstration is delivered on how the proposed reliability model may be applied in data analysis of the strength data for single carbon fibers test data.

Classical and Bayesian estimation for Topp Leone inverse Rayleigh distribution

Classical and Bayesian estimation for Topp Leone inverse Rayleigh distribution

The odd Fréchet inverse Rayleigh distribution: statistical properties and applications

The odd Fréchet inverse Rayleigh distribution: statistical properties and applications

Further Developments on the (EG) Exponential-MIR Class of Distributions

The Modified Inverse Rayleigh (MIR) distribution appeared in [Khan, M. S. (2014).Modified inverse Rayleigh distribution. International Journal of Computer Applications, 87(13):28–33] who got some theoretical properties of this distribution, and in[Nasiru, S., Mwita, P. N. and Ngesa, O. (2017). Exponentiated Generalized Exponential Dagum Distribution. Journal of King Saud University- Science, In Press] they introduced the (EG) Exponential-X class of distributions and obtained some theoretical properties with application. By assuming the random variable X follows the MIR distribution, some theoretical properties with application of the (EG) Exponential-MIR Class of distributions appeared in [Nasiru, S., Mwita, P. N. and Ngesa, O. (2018). Discussion on Generalized Modified Inverse Rayleigh Distribution. Applied Mathematics and Information Sciences, 12(1):113-124]. In the present paper we propose some extensions of the (EG) Exponential-MIR class of distributions. The (EG) Exponential- MIR class of distributions is part of Chapter 5 [Nasiru, S. (2018). A New Generalization of Transformed-Transformer Family of Distributions. Doctor of Philosophy thesis in Mathematics (Statistics Option). Pan African University, Institute for Basic Sciences, Technology and Innovation, Kenya], where the naming convention “NEGMIR” is used Keywords: T-X (W) family of distributions; Exponentiated Generalized distributions; Modified Inverse Rayleigh distribution; biological data; health data

Transmuted Generalized Inverse Rayleigh Distribution and Its Applications to Medical Science and Engineering

Transmuted Generalized Inverse Rayleigh Distribution and Its Applications to Medical Science and Engineering

Time Control Chart for Two Inverted Models

Control charts are one of the powerful techniques of Statistical Process Control. Control charts are widely accepted and applied in industry which can be used to improve productivity, prevent defects and unnecessary process adjustment. Moreover, they also provide information in diagnosis and process capability. Life time data generally contain the failure times of sample products or inter failure times or number of failures experienced in a given time. The time to failure of a product is to be considered as a quality characteristic to assess the quality of the product. Control limits are evaluated for the time to failure. In this paper the time to failure of a product is considered to follow Inverse Rayleigh and Inverse Half Logistic distributions. Life time data are compared with the control limits to judge the quality performance of the product.

Pivotal inference for the inverse Rayleigh distribution based on general progressively Type-II censored samples

ABSTRACTIn this paper, we consider the problem of estimating the scale parameter of the inverse Rayleigh distribution based on general progressively Type-II censored samples and progressively Type-II censored samples. The pivotal quantity method is used to derive the estimator of the scale parameter. Besides, considering that the maximum likelihood estimator is tough to obtain for this distribution, we derive an explicit estimator of the scale parameter by approximating the likelihood equation with Taylor expansion. The interval estimation is also studied based on pivotal inference. Then we conduct Monte Carlo simulations and compare the performance of different estimators. We demonstrate that the pivotal inference is simpler and more effective. The further application of the pivotal quantity method is also discussed theoretically. Finally, two real data sets are analyzed using our methods.