scholarly journals A New Technique for Generating Distributions Based on a Combination of Two Techniques: Alpha Power Transformation and Exponentiated T-X Distributions Family

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 412 ◽  
Author(s):  
Hadeel S. Klakattawi ◽  
Wedad H. Aljuhani
Keyword(s):  
Hazard Function ◽  
Real Data ◽  
Parameter Distribution ◽  
Data Sets ◽  
Alpha Power ◽  
Simulation Studies ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Exponentiated Weibull ◽  
A New Technique

In the following article, a new five-parameter distribution, the alpha power exponentiated Weibull-exponential distribution is proposed, based on a newly developed technique. It is of particular interest because the density of this distribution can take various symmetric and asymmetric possible shapes. Moreover, its related hazard function is tractable and showing a great diversity of asymmetrical shaped, including increasing, decreasing, near symmetrical, increasing-decreasing-increasing, increasing-constant-increasing, J-shaped, and reversed J-shaped. Some properties relating to the proposed distribution are provided. The inferential method of maximum likelihood is employed, in order to estimate the model’s unknown parameters, and these estimates are evaluated based on various simulation studies. Moreover, the usefulness of the model is investigated through its application to three real data sets. The results show that the proposed distribution can, in fact, better fit the data, when compared to other competing distributions.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals The Alpha Power Transformation Family: Properties and Applications

2019 ◽  
pp. 525-545 ◽  
Author(s):  
Mohamed E. Mead ◽  
Gauss M. Cordeiro ◽  
Ahmed Z. Afify ◽  
Hazem Al Mofleh
Keyword(s):  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Weibull Distributions ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Modified Weibull

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

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.

scholarly journals Transmuted Singh-Maddala Distribution: A new Flexible and Upside-Down Bathtub Shaped Hazard Function Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Mirza Naveed Shahzad ◽  
Faton Merovci ◽  
Zahid Asghar
Keyword(s):  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Function ◽  
Data Sets ◽  
Distribution Models ◽  
Unknown Parameters ◽  
Bathtub Shape ◽  
Parent Distribution ◽  
Special Cases

The Singh-Maddala distribution is very popular to analyze the data on income, expenditure, actuarial, environmental, and reliability related studies. To enhance its scope and application, we propose four parameters transmutedSingh-Maddala distribution, in this study. The proposed distribution is relatively more flexible than the parent distribution to model a variety of data sets. Its basic statistical properties, reliability function, and behaviors of the hazard function are derived. The hazard function showed the decreasing and an upside-down bathtub shape that is required in various survival analysis. The order statistics and generalized TL-moments with their special cases such as L-, TL-, LL-, and LH-moments are also explored. Furthermore, the maximum likelihood estimation is used to estimate the unknown parameters of the transmuted Singh-Maddala distribution. The real data sets are considered to illustrate the utility and potential of the proposed model. The results indicate that the transmuted Singh-Maddala distribution models the datasets better than its parent distribution.

scholarly journals Marshall-Olkin Alpha Power Rayleigh Distribution: Properties, Characterizations, Estimation and Engineering applications

2021 ◽  
pp. 745-760
Author(s):  
Ehab Mohamed Almetwally ◽  
Ahmed Z. Afify ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Alpha Power ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Estimation ◽  
Proposed Model

In this paper, we introduce a new there-parameter Rayleigh distribution, called the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution. Some statistical properties of the MOAPR distribution are obtained. The proposed model is characterized based on truncated moments and reverse hazard function. The maximum likelihood and bootstrap estimation methods are considered to estimate the MOPAR parameters. A Monte Carlo simulation study is performed to compare the maximum likelihood and bootstrap estimation methods. Superiority of the MOAPR distribution over some well-known distributions is illustrated by means of two real data sets.

scholarly journals On the Alpha Power Kumaraswamy Distribution: Properties, Simulation and Application

2020 ◽  
Vol 43 (2) ◽  
pp. 285-313
Author(s):  
Mohamed Ali Ahmed
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Simulation Studies ◽  
Data Set ◽  
Kumaraswamy Distribution ◽  
Mathematical Properties

Adding  new  parameters to  classical distributions becomes one  of  the most  important methods  for  increasing distributions flexibility,  especially, in  simulation   studies   and real data sets. In this paper, alpha power  transformation (APT) is used  and  applied  to  the Kumaraswamy (K) distribution and a proposed distribution, so called the alpha power Kumaraswamy (AK) distribution, is presented.  Some important mathematical properties are derived, parameters estimation of the AK distribution using maximum likelihood  method  is considered. A simulation study and  a  real  data   set  are  used  to  illustrate the  flexibility of the  AK distribution compared with other  distributions.

scholarly journals Extended Poisson-Pareto Type II Distribution: Theoretical and Computational Aspects

2019 ◽  
pp. 713-730
Author(s):  
Rania Hassan Abd El Khaleq
Keyword(s):  
Poisson Model ◽  
Real Data ◽  
Continuous Model ◽  
Data Sets ◽  
Type Ii ◽  
Unknown Parameters ◽  
New Model ◽  
Method Of Maximum Likelihood ◽  
Computational Aspects ◽  
Better Than

We introduce a new continuous model with strong physical motivations and wide applications upon compounding the diecreate zero truncated Poisson model and a new continuous model called the Burr X Pareto type II distribution. Some of its mathematical and statistical properties are derived as well as four applications to real data sets are provided with detailes to illustrate the wide importance of the new model. We conclude that the new model is better than other nine competitive models via the four applications. Method of maximum likelihood is used to estimate the unknown parameters of the new model. The new model provide adequate Öts as compared to other related models in the four applications.

scholarly journals The Truncated Power Lomax Distribution: Properties and Applications

2018 ◽  
Vol 16 (9) ◽  
pp. 655-668
Author(s):  
Sirinapa ARYUYUEN ◽  
Winai BODHISUWAN
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
The Other ◽  
Data Sets ◽  
Truncated Distribution ◽  
Unknown Parameters ◽  
Lomax Distribution

A new truncated distribution, called the truncated power Lomax (TPL) distribution, is proposed. This is a truncated version of the power Lomax distribution. The TPL distribution has increasing and decreasing shapes of the hazard function. Some statistical properties, such as moments, survival, hazard, and quantile functions, are discussed. The maximum likelihood estimation (MLE) is constructed for estimating the unknown parameters of the TPL distribution. Moreover, the distribution has been fitted with real data sets to illustrate the usefulness of the proposed distribution. From the results of the example applications, the TPL distribution provides a consistently better fit than the other distributions, i.e., power Lomax and Lomax.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

scholarly journals Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 28-45
Author(s):  
Vasili B.V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Entropy Measures ◽  
Modeling Behavior

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

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