Estimations and Prediction for the Compound Rayleigh Distribution Based on Upper Record Values

2018 ◽  
Vol 15 (2) ◽  
pp. 711-718 ◽  
Author(s):  
M. M. Badr
Keyword(s):  
Prediction Interval ◽  
Record Values ◽  
Rayleigh Distribution ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Upper Record Values ◽  
Upper Record ◽  
Two Parameters ◽  
Compound Rayleigh Distribution

This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on upper record values. We have derived the maximum likelihood (ML) and Bayesian estimators for the unknown two parameters, as well as the reliability and hazard functions. We obtained Bayes estimators on the basis of the symmetric (squared error) and asymmetric (linear exponential (LINEX) and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Furthermore, Bayesian prediction interval of the future upper record values are discussed and obtained. Finally, estimation of the parameters, practical examples of real record values and simulated record values are given to illustrate the theoretical results of prediction interval.

Inference about Weibull Distribution Using Upper Record Values

2015 ◽  
Vol 22 (04) ◽  
pp. 1550016
Author(s):  
Kai Huang ◽  
Jie Mi
Keyword(s):  
Weibull Distribution ◽  
Prediction Interval ◽  
Record Values ◽  
Testing Procedures ◽  
Scale Parameters ◽  
Upper Record Values ◽  
Record Value ◽  
Upper Record ◽  
Two Parameters ◽  
Two Parameter

This paper studies the frequentist inference about the shape and scale parameters of the two-parameter Weibull distribution using upper record values. The exact sampling distribution of the MLE of the shape parameter is derived. The asymptotic normality of the MLEs of both parameters are obtained. Based on these results this paper proposes various confidence intervals of the two parameters. Assuming one parameter is known certain testing procedures are proposed. Furthermore, approximate prediction interval for the immediately consequent record value is derived too. Conclusions are made based on intensive simulations.

scholarly journals Exact Interval Inference for the Two-Parameter Rayleigh Distribution Based on the Upper Record Values

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Jung-In Seo ◽  
Jae-Woo Jeon ◽  
Suk-Bok Kang
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Real Data ◽  
Record Values ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Upper Record Values ◽  
Upper Record ◽  
Two Parameter

The maximum likelihood method is the most widely used estimation method. On the other hand, it can produce substantial bias, and an approximate confidence interval based on the maximum likelihood estimator cannot be valid when the sample size is small. Because the sizes of the record values are considerably smaller than the original sequence observed in the majority of cases, a method appropriate for this situation is required for precise inference. This paper provides the exact confidence intervals for unknown parameters and exact predictive intervals for the future upper record values by providing some pivotal quantities in the two-parameter Rayleigh distribution based on the upper record values. Finally, the validity of the proposed inference methods was examined from Monte Carlo simulations and real data.

scholarly journals Bayesian Estimation of Stress Strength Reliability using Upper Record Values from Generalised Inverted Exponential Distribution

2019 ◽  
Vol 4 (4) ◽  
pp. 882-894
Author(s):  
Ritu Kumari ◽  
Kalpana K. Mahajan ◽  
Sangeeta Arora
Keyword(s):  
Exponential Distribution ◽  
Simulated Data ◽  
Record Values ◽  
Data Sets ◽  
Bayes Estimators ◽  
Informative Prior ◽  
Upper Record Values ◽  
Upper Record ◽  
Hpd Intervals ◽  
Simulated Data Sets

The paper develops Bayesian estimators and HPD intervals for the stress strength reliability of generalised inverted exponential distribution using upper record values. For prior distribution, informative prior as well as non-informative prior both are considered. The Bayes estimators are obtained under both symmetric and asymmetric loss functions. A simulation study is conducted to obtain the Bayes estimates of stress strength reliability. Simulated data sets are also considered here for illustration purpose.

scholarly journals Bayesian Estimation for Nadarajah-Haghighi Distribution Based on Upper Record Values

2019 ◽  
pp. 217-230
Author(s):  
MS Sana ◽  
M. Faizan
Keyword(s):  
Prior Information ◽  
Record Values ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Jeffreys Prior ◽  
Unknown Parameters ◽  
R Software ◽  
Squared Error ◽  
Upper Record Values ◽  
Upper Record

This paper discusses maximum likelihood and Bayes estimation of the two unknown parameters of Nadarajah and Haghighi distribution based on record values. Different Bayes estimates are derived under squared error, balanced squared error and general entropy loss functions by using Jeffreys' prior information and extension of Jeffreys' prior information. It is observed that the associated posterior distribution appears in an intractable form. So, we have used Tierney and Kadane approximation method to compute these estimates. Finally, numerical computations are presented based on generated record values using R software.

scholarly journals Some Characterizations of the Distribution of the Condition Number of a Complex Gaussian Matrix

2020 ◽  
Vol 8 (1) ◽  
pp. 22-35
Author(s):  
M. Shakil ◽  
M. Ahsanullah
Keyword(s):  
Order Statistics ◽  
Condition Number ◽  
Record Values ◽  
Distributional Properties ◽  
Upper Record Values ◽  
Upper Record

AbstractThe objective of this paper is to characterize the distribution of the condition number of a complex Gaussian matrix. Several new distributional properties of the distribution of the condition number of a complex Gaussian matrix are given. Based on such distributional properties, some characterizations of the distribution are given by truncated moment, order statistics and upper record values.

scholarly journals Nonparametric Prediction Intervals of generalized order statistics from two independent sequences

2016 ◽  
Vol 4 (1) ◽  
pp. 36 ◽  
Author(s):  
Mostafa Mohie El-Din ◽  
Walid Emam
Keyword(s):  
Order Statistics ◽  
Record Values ◽  
Prediction Intervals ◽  
Generalized Order Statistics ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
Nonparametric Prediction ◽  
Nonparametric Prediction Intervals ◽  
Generalized Order

<p>This paper, discusses the problem of predicting future a generalized order statistic of an iid sequence sample was drawn from an arbitrary unknown distribution, based on observed also generalized order statistics from the same population. The coverage probabilities of these prediction intervals are exact and free of the parent distribution F(). Prediction formulas of ordinary order statistics and upper record values are extracted as special cases from the productive results. Finally, numerical computations on several models of ordered random variables are given to illustrate the proposed procedures.</p>

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