scholarly journals Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Fuad S. Al-Duais ◽  
Mohammed Alhagyan
Keyword(s):  
Nonlinear Programming ◽  
Loss Function ◽  
Record Values ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Balanced Loss Function ◽  
Lower Record ◽  
Lower Record Values ◽  
Mean Square Errors ◽  
Balanced Loss Functions

Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function.

scholarly journals Estimation of R for geometric distribution under lower record values

2020 ◽  
Vol 18 (6) ◽  
pp. 368-375
Author(s):  
M. O. Mohamed
Keyword(s):  
Bayesian Methods ◽  
Prior Information ◽  
Geometric Distribution ◽  
Record Values ◽  
Loss Functions ◽  
Likelihood Estimator ◽  
Illustrative Purpose ◽  
Lower Record ◽  
Lower Record Values ◽  
Mean Square Errors

In this paper, the estimation of the stress-strength model R=P(Y<X), based on lower record values is derived when both X and Y are independent and identical random variables with geometric distribution. Estimating R with maximum likelihood estimator and Bayes estimator with non-informative prior information based on mean square errors and LINIX loss functions for geometric distribution are obtained. The confidence intervals of R are constructed by using exact, bootstrap and Bayesian methods. Finally, different methods have been used for illustrative purpose by using simulation. The main results are obtained and introduced through a set of tables and figures with discussions.

scholarly journals Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Bahman Tarvirdizade ◽  
Hossein Kazemzadeh Garehchobogh
Keyword(s):  
Maximum Likelihood ◽  
Empirical Bayes ◽  
Interval Estimation ◽  
Record Values ◽  
Rayleigh Distribution ◽  
Bayes Estimators ◽  
Credible Sets ◽  
Lower Record ◽  
Lower Record Values ◽  
Empirical Bayes Estimators

We consider the estimation of stress-strength reliability based on lower record values when X and Y are independently but not identically inverse Rayleigh distributed random variables. The maximum likelihood, Bayes, and empirical Bayes estimators of R are obtained and their properties are studied. Confidence intervals, exact and approximate, as well as the Bayesian credible sets for R are obtained. A real example is presented in order to illustrate the inferences discussed in the previous sections. A simulation study is conducted to investigate and compare the performance of the intervals presented in this paper and some bootstrap intervals.

scholarly journals A Bayesian Approach for Estimating Parameter of Rayleigh Distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 23-39
Author(s):  
J. Mahanta ◽  
M. B. A. Talukdar
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Bayesian Approach ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Risk ◽  
Squared Error ◽  
Different Types ◽  
Two Parameters ◽  
Special Case

This paper is concerned with estimating the parameter of Rayleigh distribution (special case of two parameters Weibull distribution) by adopting Bayesian approach under squared error (SE), LINEX, MLINEX loss function. The performances of the obtained estimators for different types of loss functions are then compared. Better result is found in Bayesian approach under MLINEX loss function. Bayes risk of the estimators are also computed and presented in graphs.

scholarly journals A Characterization and Recurrence Relations of Moments of the Size-Biased Power Function Distribution by Lower Record Values

2018 ◽  
Vol 7 (5) ◽  
pp. 1
Author(s):  
Shakila Bashir ◽  
Mujahid Rasul
Keyword(s):  
Power Function ◽  
Recurrence Relations ◽  
Survival Function ◽  
Joint Probability ◽  
Record Values ◽  
Cumulative Distribution ◽  
Function Distribution ◽  
Power Function Distribution ◽  
Lower Record ◽  
Lower Record Values

A variety of research papers have been published on record values from various continuous distributions. This paper investigated lower record values from the size-biased power function distribution (LR-SPFD). Some basic properties including moments, skewness, kurtosis, Shannon entropy, cumulative distribution function, survival function and hazard function of the lower record values from SPFD have been discussed. The joint probability density function (pdf) of $n^{th}$ and $m^{th}$ lower record values from SPFD is developed. Recurrence relations of the single and product moments of the LR-SPFD have been derived. A characterization of the lower record values from SPFD is also developed.

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