scholarly journals A New Generator of Probability Models: The Exponentiated Sine-G Family for Lifetime Studies

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1394
Author(s):  
Mustapha Muhammad ◽  
Huda M. Alshanbari ◽  
Ayed R. A. Alanzi ◽  
Lixia Liu ◽  
Waqas Sami ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Weibull Model ◽  
Mean Square ◽  
Reliability Parameter ◽  
Coverage Probabilities ◽  
The Mean

In this article, we propose the exponentiated sine-generated family of distributions. Some important properties are demonstrated, such as the series representation of the probability density function, quantile function, moments, stress-strength reliability, and Rényi entropy. A particular member, called the exponentiated sine Weibull distribution, is highlighted; we analyze its skewness and kurtosis, moments, quantile function, residual mean and reversed mean residual life functions, order statistics, and extreme value distributions. Maximum likelihood estimation and Bayes estimation under the square error loss function are considered. Simulation studies are used to assess the techniques, and their performance gives satisfactory results as discussed by the mean square error, confidence intervals, and coverage probabilities of the estimates. The stress-strength reliability parameter of the exponentiated sine Weibull model is derived and estimated by the maximum likelihood estimation method. Also, nonparametric bootstrap techniques are used to approximate the confidence interval of the reliability parameter. A simulation is conducted to examine the mean square error, standard deviations, confidence intervals, and coverage probabilities of the reliability parameter. Finally, three real applications of the exponentiated sine Weibull model are provided. One of them considers stress-strength data.

scholarly journals ESTIMASI PARAMETER DISTRIBUSI EKPONENSIAL PADA LOKASI TERBATAS

2007 ◽  
Vol 1 (2) ◽  
pp. 1-7
Author(s):  
Mozart W. Talakua ◽  
Jefri Tipka
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Mean Square Error ◽  
Likelihood Estimation ◽  
Consistent Estimator ◽  
Parameter Distribution ◽  
Mean Square ◽  
The Common ◽  
The Mean ◽  
Best Estimator

The common method in Estimating Parameter Distribution Exponential at Finite Location is Maximum Likelihood Estimation (MLE).The best estimator is consistent estimator. Because of The Mean Square Error (MSE) can be used in comparing some detectable estimators that it had looking for with Maximum Likelihood Estimation (MLE) so can find the consistent estimator in Estimating Parameter Distribution Exponential At Finite Location

scholarly journals A Note on the Existence of the Location Parameter Estimate of the Three-Parameter Weibull Model Using the Weibull Plot

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Chanseok Park
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Weibull Model ◽  
Parameter Estimate ◽  
Reliability Engineering ◽  
Bounded Interval ◽  
Weibull Plot ◽  
Sample Correlation

The Weibull model is one of the widely used distributions in reliability engineering. For the parameter estimation of the Weibull model, there are several existing methods. The method of the maximum likelihood estimation among others is preferred because of its attractive statistical properties. However, for the case of the three-parameter Weibull model, the method of the maximum likelihood estimation has several drawbacks. To avoid the drawbacks, the method using the sample correlation from the Weibull plot is recently suggested. In this paper, we provide the justification for using this new method by showing that the location estimate of the three-parameter Weibull model exists in a bounded interval.

A New Approach to Estimating Populations by the Removal Method

1983 ◽  
Vol 40 (12) ◽  
pp. 2153-2169 ◽  
Author(s):  
Jon Schnute
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
New Brunswick ◽  
Population Size ◽  
Confidence Intervals ◽  
Likelihood Estimation ◽  
Data Interpretation ◽  
Population Estimate ◽  
New Approach ◽  
Removal Method

This paper presents a new approach to the use of removal data in estimating the size of a population of fish or other animals. The theory admits a variety of assumptions on how catchability varies among fishings including the assumption of constant catchability, which underlies most previous work. The methods here hinge on maximum likelihood estimation, and they can be used both to decide objectively if the data justify rejecting constant catchability and to determine confidence intervals for the parameters. The work includes a new method of assigning confidence to the population estimate and points out problems with methods currently available in the literature, even in the case of constant catchability. The theory is applied both to data in historical literature and to more recent data from streams in New Brunswick, Canada. These examples demonstrate that the assumption of constant catchability can frequently lead to serious errors in data interpretation. In some cases, the conclusion that the population size is well known may be blatantly false, and reasonable estimates may be impossible without further data.

scholarly journals "Evaluation of Some Methods for Estimating the Weibull Distribution Parameters"

2017 ◽  
Vol 4 (2) ◽  
pp. 8-14
Author(s):  
J. A. Labban ◽  
H. H. Depheal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Mean Square Error ◽  
Random Sample ◽  
Likelihood Estimation ◽  
Mean Square ◽  
Distribution Parameters

"This paper some of different methods to estimate the parameters of the 2-Paramaters Weibull distribution such as (Maximum likelihood Estimation, Moments, Least Squares, Term Omission). Mean square error will be considered to compare methods fits in case to select the best one. There by simulation will be implemented to generate different random sample of the 2-parameters Weibull distribution, those contain (n=10, 50, 100, 200) iteration each 1000 times."

scholarly journals The Kumaraswamy Exponentiated U-Quadratic Distribution: Properties and Application

2018 ◽  
pp. 1-17
Author(s):  
Mustapha Muhammad ◽  
Isyaku Muhammad ◽  
Aisha Muhammad Yaya
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Alternative Methods ◽  
Finite Sample ◽  
Modified Maximum Likelihood ◽  
Probability Weighted Moments

In this paper, a new lifetime model called Kumaraswamy exponentiated U-quadratic (KwEUq) distribution is proposed. Several mathematical and statistical properties are derived and studied such as the explicit form of the quantile function, moments, moment generating function, order statistics, probability weighted moments, Shannon entropy and Renyi entropy. We also found that the usual maximum likelihood estimates (MLEs) fail to hold for the KwEUq distribution. Two alternative methods are suggested for the parameter estimation of the KwEUq, the alternative maximum likelihood estimation (AMLE) and modified maximum likelihood estimation (MMLE). Simulation studies were conducted to assess the finite sample behavior of the AMLEs and MMLEs. Finally, we provide application of the KwEUq for illustration purposes.

New Testifying Method of Unit Weight Mean Square Error of No-Equal Precision Independent Surveying Values

2012 ◽  
Vol 170-173 ◽  
pp. 2904-2907 ◽  
Author(s):  
Yong He Deng
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
New Method ◽  
Unit Weight ◽  
Mean Square ◽  
Maximum Likelihood Estimation Method

For unit weight mean square error of no-equal precision independent surveying values,this paper summed up several old estifying methods, pointed out their scarcities or mistakes, and advanced a sort of new method- maximum likelihood estimation method which is simple and strict.This is useful for theory of unit weight mean square error of no-equal precision independent surveying values to be perfect and for college surveying textbook to be improved and unified.

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