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.

scholarly journals The Topp-Leone Generalized Inverted Exponential Distribution with Real Data Applications

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1144
Author(s):  
Zakeia A. Al-Saiary ◽  
Rana A. Bakoban
Keyword(s):  
Maximum Likelihood ◽  
Survival Function ◽  
Information Matrix ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Mean Deviation ◽  
Data Sets ◽  
Unknown Parameters ◽  
Illustrative Purpose

In this article, a new three parameters lifetime model called the Topp-Leone Generalized Inverted Exponential (TLGIE) Distribution is introduced. Various properties of the model are derived, including moments, quantile function, survival function, hazard rate function, mean deviation and mode. The method of maximum likelihood is used to estimate the unknown parameters. The properties of the maximum likelihood estimators using Fisher information matrix are studied. Three real data sets are applied for illustrative purpose of this study.

scholarly journals Maximum likelihood estimation based on type-i hybrid progressive censored competing risks data

2016 ◽  
Vol 4 (1) ◽  
pp. 20
Author(s):  
Samir Ashour ◽  
Wael Abu El Azm
Keyword(s):  
Maximum Likelihood ◽  
Competing Risks ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Data Set ◽  
Special Cases ◽  
Competing Risks Data

<p>This paper is concerned with the estimators problems of the generalized Weibull distribution based on Type-I hybrid progressive censoring scheme (Type-I PHCS) in the presence of competing risks when the cause of failure of each item is known. Maximum likelihood estimates and the corresponding Fisher information matrix are obtained. We generalized Kundu and Joarder [7] results in the case of the exponential distribution while, the corresponding results in the case of the generalized exponential and Weibull distributions may be obtained as a special cases. A real data set is used to illustrate the theoretical results.</p>

scholarly journals Kumaraswamy Distribution Based on Alpha Power Transformation Methods

2021 ◽  
pp. 14-29
Author(s):  
H. E. Hozaien ◽  
G. R. AL Dayian ◽  
A. A. EL-Helbawy
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Mean Residual Life ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Data Set ◽  
Kumaraswamy Distribution

In this paper, the alpha power Kumaraswamy distribution, new alpha power transformed Kumaraswamy distribution and new extended alpha power transformed Kumaraswamy distribution are presented. Some statistical properties of the three distributions are derived including quantile function, moments and moment generating function, mean residual life and order statistics. Estimation of the unknown parameters based on maximum likelihood estimation are obtained. A simulation study is carried out. Finally, a real data set is applied.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals The New Novel Discrete Distribution with Application on COVID-19 Mortality Numbers in Kingdom of Saudi Arabia and Latvia

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
M. Nagy ◽  
Ehab M. Almetwally ◽  
Ahmed M. Gemeay ◽  
Heba S. Mohammed ◽  
Taghreed M. Jawa ◽  
...  
Keyword(s):  
Saudi Arabia ◽  
Statistical Model ◽  
Discrete Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Linear Representation ◽  
Quantile Function ◽  
Mortality Data ◽  
Unknown Parameters ◽  
New Novel

This paper aims to introduce a superior discrete statistical model for the coronavirus disease 2019 (COVID-19) mortality numbers in Saudi Arabia and Latvia. We introduced an optimal and superior statistical model to provide optimal modeling for the death numbers due to the COVID-19 infections. This new statistical model possesses three parameters. This model is formulated by combining both the exponential distribution and extended odd Weibull family to formulate the discrete extended odd Weibull exponential (DEOWE) distribution. We introduced some of statistical properties for the new distribution, such as linear representation and quantile function. The maximum likelihood estimation (MLE) method is applied to estimate the unknown parameters of the DEOWE distribution. Also, we have used three datasets as an application on the COVID-19 mortality data in Saudi Arabia and Latvia. These three real data examples were used for introducing the importance of our distribution for fitting and modeling this kind of discrete data. Also, we provide a graphical plot for the data to ensure our results.

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.

The Odd Log-Logistic Log-Normal Distribution with Theory and Applications

2018 ◽  
Vol 10 (04) ◽  
pp. 1850009 ◽  
Author(s):  
Gamze Ozel ◽  
Emrah Altun ◽  
Morad Alizadeh ◽  
Mahdieh Mozafari
Keyword(s):  
Normal Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Quantile Function ◽  
Logistic Distribution ◽  
Unknown Parameters ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occuring in practical situations. The proposed distribution is derived from the log-normal distribution, by using odd log-logistic distribution. Statistical properties of this distribution, including hazard function, moments, quantile function, and asymptotics, are derived. The unknown parameters are estimated by the maximum likelihood estimation procedure. For different parameter settings and sample sizes, a simulation study is performed and the performance of the new distribution is compared to beta log-normal. The new lifetime model can be very useful and its superiority is illustrated by means of two real data sets.

scholarly journals The Half-Logistic Lomax Distribution for Lifetime Modeling

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Jawaria Zahoor
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Information Matrix ◽  
Simulated Data ◽  
Quantile Function ◽  
Rate Function ◽  
Mean Residual Life ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Proposed Model

We introduce a new two-parameter lifetime distribution called the half-logistic Lomax (HLL) distribution. The proposed distribution is obtained by compounding half-logistic and Lomax distributions. We derive some mathematical properties of the proposed distribution such as the survival and hazard rate function, quantile function, mode, median, moments and moment generating functions, mean deviations from mean and median, mean residual life function, order statistics, and entropies. The estimation of parameters is performed by maximum likelihood and the formulas for the elements of the Fisher information matrix are provided. A simulation study is run to assess the performance of maximum-likelihood estimators (MLEs). The flexibility and potentiality of the proposed model are illustrated by means of real and simulated data sets.

scholarly journals The Half-Logistic Generalized Weibull Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Amna Bibi
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Type I ◽  
Failure Rate Function ◽  
New Model ◽  
Compound Distribution

A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher’s information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

scholarly journals The Three-parameters Marshall-Olkin Generalized Weibull Model with Properties and Different Applications to Real Data Sets

2020 ◽  
pp. 675-688
Author(s):  
Mohamed G. Khalil ◽  
Wagdy M. Kamel
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Weibull Model ◽  
Parametric Model ◽  
Data Sets ◽  
Unknown Parameters ◽  
Graphical Simulation ◽  
Method Of Maximum Likelihood ◽  
New Distribution

A new three-parameter life parametric model called the Marshall-Olkin generalized Weibull is defined and studied. Relevant properties are mathematically derived and analyzed. The new density exhibits various important symmetric and asymmetric shapes with different useful kurtosis. The new failure rate can be “constant”, “upside down-constant (reversed U-HRF-constant)”, “increasing then constant”, “monotonically increasing”, “J-HRF” and “monotonically decreasing”. The method of maximum likelihood is employed to estimate the unknown parameters. A graphical simulation is performed to assess the performance of the maximum likelihood estimation. We checked and proved empirically the importance, applicability and flexibility of the new Weibull model in modeling various symmetric and asymmetric types of data. The new distribution has a high ability to model different symmetric and asymmetric types of data.

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