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.

Maximum Likelihood Estimation Modeling of Welded Joints Based on Metal Magnetic Memory Parameters

2016 ◽  
Vol 853 ◽  
pp. 458-462
Author(s):  
Hai Yan Xing ◽  
Hua Ge ◽  
Guan Ga Dai ◽  
Zheng Shuai Yu ◽  
Xiao Jun Sun
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Normal State ◽  
Kernel Density ◽  
Likelihood Estimation ◽  
Magnetic Memory ◽  
Metal Magnetic Memory ◽  
Damage State ◽  
Modified Maximum Likelihood ◽  
Density Values

In order to quantitatively identify critical hidden damage for weld joints by using the metal magnetic memory technology (MMM), the modified maximum likelihood estimation MMM model is first proposed. The experimental materials are Q235B welded plate specimens. Fatigue tension experiments were operated to find the MMM feature laws of critical hidden damage by comparing with synchronous X-ray detection results. Four MMM characteristic parameters, that is, ΔHp(y) , Kymax , mmax and S(K), are extracted corresponding to the normal state and the hidden damage state, respectively. The probability density values of ΔHp(y) , Kymax , mmax and S(K)are calculated by the optimized bandwidth kernel density estimation. The quantitative maximum likelihood estimation MMM model is established based on optimized bandwidth kernel density. The verification result shows the maximum likelihood value of hidden damage state is twice as much as that of the normal state, which is consistent with the practical results. This provides a new method for quantitative MMM identification of weld critical hidden damages.

The Estimated Probability of Dizygotic Twins: A Comparison of Two Methods

2009 ◽  
Vol 12 (1) ◽  
pp. 79-85 ◽  
Author(s):  
Jill Hardin ◽  
Steve Selvin ◽  
Suzan L. Carmichael ◽  
Gary M. Shaw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Data Sources ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Dizygotic Twin ◽  
Twin Data ◽  
Dizygotic Twins ◽  
The Relationship

AbstractThis study presents a general model of two binary variables and applies it to twin sex pairing data from 21 twin data sources to estimate the frequency of dizygotic twins. The purpose of this study is to clarify the relationship between maximum likelihood and Weinberg's differential rule zygosity estimation methods. We explore the accuracy of these zygosity estimation measures in relation to twin ascertainment methods and the probability of a male. Twin sex pairing data from 21 twin data sources representing 15 countries was collected for use in this study. Maximum likelihood estimation of the probability of dizygotic twins is applied to describe the variation in the frequency of dizygotic twin births. The differences between maximum likelihood and Weinberg's differential rule zygosity estimation methods are presented as a function of twin data ascertainment method and the probability of a male. Maximum likelihood estimation of the probability of dizygotic twins ranges from 0.083 (95% approximate CI: 0.082, 0.085) to 0.750 (95% approximate CI: 0.749, 0.752) for voluntary ascertainment data sources and from 0.374 (95% approximate CI: 0.373, 0.375) to 0.987 (95% approximate CI: 0.959, 1.016) for active ascertainment data sources. In 17 of the 21 twin data sources differences of 0.01 or less occur between maximum likelihood and Weinberg zygosity estimation methods. The Weinberg and maximum likelihood estimates are negligibly different in most applications. Using the above general maximum likelihood estimate, the probability of a dizygotic twin is subject to substantial variation that is largely a function of twin data ascertainment method.

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 The Exponentiated Lindley Geometric Distribution with Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 510
Author(s):  
Bo Peng ◽  
Zhengqiu Xu ◽  
Min Wang
Keyword(s):  
Maximum Likelihood ◽  
Geometric Distribution ◽  
Residual Life ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters

We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

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