scholarly journals Entropy Inference Based on An Objective Bayesian Approach for Upper Record Values Having the Two-Parameter Logistic Distribution

2016 ◽  
Author(s):  
Jung-In Seo
Keyword(s):  
Bayesian Approach ◽  
Record Values ◽  
Logistic Distribution ◽  
Upper Record Values ◽  
Upper Record ◽  
Two Parameter

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 The Type I Generalized Half-Logistic Distribution Based on Upper Record Values

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Devendra Kumar ◽  
Neetu Jain ◽  
Shivani Gupta
Keyword(s):  
Maximum Likelihood ◽  
Confidence Intervals ◽  
Record Values ◽  
Maximum Likelihood Estimates ◽  
Logistic Distribution ◽  
Type I ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
First Four Moments

We consider the type I generalized half-logistic distribution and derive some new explicit expressions and recurrence relations for marginal and joint moment generating functions of upper record values. Here we show the computations for the first four moments and their variances. Next we show that results for record values of this distribution can be derived from our results as special cases. We obtain the characterization result of this distribution on using the recurrence relation for single moment and conditional expectation of upper record values. We obtain the maximum likelihood estimators of upper record values and their confidence intervals. Also, we compute the maximum likelihood estimates of the parameters of upper record values and their confidence intervals. At last, we present one real case data study to emphasize the results of this paper.

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 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>

scholarly journals Evaluating the Lifetime Performance Index Based on the Bayesian Estimation for the Rayleigh Lifetime Products with the Upper Record Values

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Wen-Chuan Lee ◽  
Jong-Wuu Wu ◽  
Ching-Wen Hong ◽  
Shie-Fan Hong
Keyword(s):  
Loss Function ◽  
Performance Index ◽  
Resource Planning ◽  
Record Values ◽  
Testing Procedure ◽  
Assessment System ◽  
Squared Error Loss Function ◽  
Lifetime Performance ◽  
Upper Record Values ◽  
Upper Record

Quality management is very important for many manufacturing industries. Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. Hence, the lifetime performance indexCLis utilized to measure the performance of product, whereLis the lower specification limit. This study constructs a Bayesian estimator ofCLunder a Rayleigh distribution with the upper record values. The Bayesian estimations are based on squared-error loss function, linear exponential loss function, and general entropy loss function, respectively. Further, the Bayesian estimators ofCLare utilized to construct the testing procedure forCLbased on a credible interval in the condition of knownL. The proposed testing procedure not only can handle nonnormal lifetime data, but also can handle the upper record values. Moreover, the managers can employ the testing procedure to determine whether the lifetime performance of the Rayleigh products adheres to the required level. The hypothesis testing procedure is a quality performance assessment system in enterprise resource planning (ERP).

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