scholarly journals On the Extension of Exponentiated Pareto Distribution

2021 ◽  
Vol 19 (1) ◽  
pp. 2-26
Author(s):  
Amal S. Hassan ◽  
Saeed Elsayed Hemeda ◽  
Said G. Nassr
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Simulation Study ◽  
Pareto Distribution ◽  
Weighted Least Squares ◽  
Real Data ◽  
Statistical Properties ◽  
Bayesian Estimators

In this study, an extended exponentiated Pareto distribution is proposed. Some statistical properties are derived. We consider maximum likelihood, least squares, weighted least squares and Bayesian estimators. A simulation study is implemented for investigating the accuracy of different estimators. An application of the proposed distribution to a real data is presented.

Half Logistic Odd Weibull-Topp-Leone-G Family of Distributions: Model, Properties and Applications

2020 ◽  
Vol 15 (4) ◽  
pp. 2481-2510
Author(s):  
Fastel Chipepa ◽  
Divine Wanduku ◽  
Broderick Olusegun Oluyede
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Statistical Properties ◽  
Maximum Likelihood Estimates ◽  
Special Cases ◽  
Family Of Distributions

A new flexible and versatile generalized family of distributions, namely, half logistic odd Weibull-Topp-Leone-G (HLOW-TL-G) distribution is presented. The distribution can be traced back to the exponentiated-G distribution. We derive the statistical properties of the proposed family of distributions. Maximum likelihood estimates of the HLOW-TL-G family of distributions are also presented. Five special cases of the proposed family are presented. A simulation study and real data applications on one of the special cases are also presented

Cubic Transmuted-G Family of Distributions and Its Properties

2018 ◽  
Vol 33 (2) ◽  
pp. 103-112 ◽  
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Information Criteria ◽  
Data Sets ◽  
New Family ◽  
Family Of Distributions

Abstract In this article, a new family of distributions is introduced by using transmutation maps. The proposed family of distributions is expected to be useful in modeling real data sets. The genesis of the proposed family, including several statistical and reliability properties, is presented. Methods of estimation like maximum likelihood, least squares, weighted least squares, and maximum product spacing are discussed. Maximum likelihood estimation under censoring schemes is also considered. Further, we explore some special models of the proposed family of distributions and examined different properties of these special models. We compare three particular models of the proposed family with several existing distributions using different information criteria. It is observed that the proposed particular models perform better than different competing models. Applications of the particular models of the proposed family of distributions are finally presented to establish the applicability in real life situations.

scholarly journals The Odd Log-Logistic Poisson Inverse Rayleigh Distribution: Statistical Properties and Applications

2020 ◽  
pp. 775-787
Author(s):  
Ibrahim Elbatal
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Statistical Properties ◽  
Data Sets ◽  
New Model ◽  
Fundamental Properties

In this work, a new extension of the Inverse Rayleigh model is proposed and studied. We derive some of its fundamental properties. We assess the performance of the maximum likelihood estimators via a simulation study. The importance of the new model is shown via two applications to real data sets. The new model is better fit than other important competitive models based on two real data sets.

scholarly journals The New Odd Log-Logistic Generalised Half-Normal Distribution: Mathematical Properties and Simulations

2019 ◽  
pp. 277-302 ◽  
Author(s):  
Mahmoud afshari Afshari ◽  
Mosa Abdi ◽  
Hamid Karamikabir ◽  
Mahdiye Mozafari ◽  
Morad Alizadeh
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Test Validity ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Moment Generating Function ◽  
Data Sets ◽  
Least Squares Estimators ◽  
Anderson Darling

The new distributions are very useful in describing real data sets, because these distributions are more flexible to model real data that present a high degree of skewness and kurtosis. The choice of the best-suited statistical distribution for modeling data is very important.In this paper, A new class of distributions called the {\it  New odd log-logistic generalized half-normal} (NOLL-GHN) family with four parameters is introduced and studied. This model contains  sub-models  such as  half-normal (HN), generalized half-normal (GHN )and odd log-logistic generalized half-normal (OLL-GHN) distributions.some statistical properties such as moments and moment generating function have been calculated.The Biases and MSE's of  estimator methods such as maximum likelihood estimators ,  least squares estimators, weighted least squares estimators,Cramer-von-Mises estimators, Anderson-Darling estimators and right tailed Anderson-Darling estimators  are calculated.The fitness capability of this model has been investigated  by fitting this model and others based on real data sets. The maximum likelihood  estimators are  assessed with simulated  real data from proposed model. We present the simulation in order to test validity of maximum likelihood estimators.

scholarly journals A new generalization of Aradhana distribution: Properties and applications

2020 ◽  
Vol 16 (2) ◽  
pp. 51-66
Author(s):  
A. Hassan ◽  
S. A. Dar ◽  
P. B. Ahmad ◽  
B. A. Para
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Real Data ◽  
Statistical Properties ◽  
Model Parameters ◽  
R Software ◽  
Data Set

AbstractIn this paper, we introduce a new generalization of Aradhana distribution called as Weighted Aradhana Distribution (WID). The statistical properties of this distribution are derived and the model parameters are estimated by maximum likelihood estimation. Simulation study of ML estimates of the parameters is carried out in R software. Finally, an application to real data set is presented to examine the significance of newly introduced model.

scholarly journals Marshll–Olkin Extended Inverse Pareto Distribution and its Application

2017 ◽  
Vol 6 (6) ◽  
pp. 71
Author(s):  
M- Gharib ◽  
B-I- Mohammed ◽  
W-E-R- Aghel
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Simulation Study ◽  
Pareto Distribution ◽  
Real Data ◽  
Failure Criteria ◽  
Data Sets ◽  
New Model ◽  
Proposed Model ◽  
Family Of Distributions

This paper introduces a new extension of the Inverse Pareto distribution along with in the framework of Marshal-Olkin (1997) family of distributions. This model is capable of modeling various shapes of aging and failure criteria. The statistical properties of the new model are discussed and the maximum likelihood and maximum product spacing’s methods are used to estimate the parameters involved. Explicit expressions are derived for the moments and the order statistics are examined for the new proposed model. Finally, the usefulness of the new model for modeling reliability data is illustrated using two real data sets with simulation study.

scholarly journals A new generalization of the inverse Lomax distribution with statistical properties and applications

2021 ◽  
Vol 8 (4) ◽  
pp. 89-97
Author(s):  
Hassan et al. ◽  
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Statistical Properties ◽  
Maximum Likelihood Estimates ◽  
Entropy Measure ◽  
Model Parameters ◽  
Lomax Distribution ◽  
Inverse Lomax Distribution ◽  
Mean Square Errors

In this paper, we introduce a new generalization of the inverse Lomax distribution with one extra shape parameter, the so-called power inverse Lomax (PIL) distribution, derived by using the power transformation method. We provide a more flexible density function with right-skewed, uni-modal, and reversed J-shapes. The new three-parameter lifetime distribution capable of modeling decreasing, Reversed-J and upside-down hazard rates shapes. Some statistical properties of the PIL distribution are explored, such as quantile measure, moments, moment generating function, incomplete moments, residual life function, and entropy measure. The estimation of the model parameters is discussed using maximum likelihood, least squares, and weighted least squares methods. A simulation study is carried out to compare the efficiencies of different methods of estimation. This study indicated that the maximum likelihood estimates are more efficient than the corresponding least squares and weighted least squares estimates in approximately most of the situations Also, the mean square errors for all estimates are decreasing as the sample size increases. Further, two real data applications are provided in order to examine the flexibility of the PIL model by comparing it with some known distributions. The PIL model offers a more flexible distribution for modeling lifetime data and provides better fits than other models such as inverse Lomax, inverse Weibull, and generalized inverse Weibull.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

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