scholarly journals A Compound Class of the Inverse Gamma and Power Series Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1328
Author(s):  
Pilar A. Rivera ◽  
Enrique Calderín-Ojeda ◽  
Diego I. Gallardo ◽  
Héctor W. Gómez
Keyword(s):  
Power Series ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Hazard Functions ◽  
New Class ◽  
Inverse Gamma ◽  
Gamma Power ◽  
Power Series Distributions ◽  
Quantile Method

In this paper, the inverse gamma power series (IGPS) class of distributions asymmetric is introduced. This family is obtained by compounding inverse gamma and power series distributions. We present the density, survival and hazard functions, moments and the order statistics of the IGPS. Estimation is first discussed by means of the quantile method. Then, an EM algorithm is implemented to compute the maximum likelihood estimates of the parameters. Moreover, a simulation study is carried out to examine the effectiveness of these estimates. Finally, the performance of the new class is analyzed by means of two asymmetric real data sets.

scholarly journals The The Topp Leone-G Power Series Class of Distributions with Applications

2021 ◽  
pp. 827-846
Author(s):  
Fastel Chipepa ◽  
Boikanyo Makubate ◽  
Broderick Oluyede ◽  
Kethamile Rannona
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Poisson Distribution ◽  
Simulation Study ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
New Class ◽  
Proposed Model ◽  
Special Case

We present a new class of distributions called the Topp-Leone-G Power Series (TL-GPS) class of distributions. This model is obtained by compounding the Topp-Leone-G distribution with the power series distribution. Statistical prop- erties of the TL-GPS class of distributions are obtained. Maximum likelihood estimates for the proposed model were obtained. A simulation study is carried out for the special case of Topp-Leone Log-Logistic Poisson distribution to assess the performance of the maximum likelihood estimates. Finally, we apply Topp-Leone-log-logistic Poisson distribution to real data sets to illustrate the usefulness and applicability of the proposed class of distributions.

scholarly journals Type II Exponentiated Half-Logistic-Topp-Leone-G Power Series Class of Distributions with Applications

2021 ◽  
pp. 885-909
Author(s):  
Thatayaone Moakofi ◽  
Broderick Oluyede ◽  
Fastel Chipepa
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Real Data ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Type Ii ◽  
Nested Models ◽  
New Class ◽  
Proposed Model

This paper aims to develop a new class of distributions, namely, type II exponentiated half-logistic Topp-Leone power series (TIIEHL-TL-GPS) class of distributions. Some important properties including moments, quantiles, moment generating function, entropy and maximum likelihood estimates are derived. A simulation is conducted study to evaluate the consistency of the maximum likelihood estimates. We also present three real data examples to illustrate the usefulness of the new class of distributions. Results shows that the proposed model performs better than nested and several non-nested models on selected data sets

scholarly journals The Exponentiated Burr XII Power Series Distribution: Properties and Applications

Stats ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 15-31
Author(s):  
Arslan Nasir ◽  
Haitham Yousof ◽  
Farrukh Jamal ◽  
Mustafa Korkmaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Power Series ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Data Sets ◽  
Power Series Distributions ◽  
New Distribution

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

scholarly journals The Exponentiated Kumaraswamy-G Class: General Properties and Application

2019 ◽  
Vol 42 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Ronaldo Silva ◽  
Frank Gomes-Silva ◽  
Manoel Ramos ◽  
Gauss Moutinho Cordeiro ◽  
Pedro Marinho ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Quantile Function ◽  
Weibull Model ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
New Class ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood

We propose a new family of distributions called the exponentiated Kumaraswamy-G class with three extra positive parameters, which generalizes the Cordeiro and de Castro's family. Some special distributions in the new class are discussed. We derive some mathematical properties of the proposed class including explicit expressions for the quantile function, ordinary and incomplete moments, generating function, mean deviations, reliability, Rényi entropy and Shannon entropy. The method of maximum likelihood is used to fit the distributions in the proposed class. Simulations are performed in order to assess the asymptotic behavior of the maximum likelihood estimates. We illustrate its potentiality with applications to two real data sets which show that the extended Weibull model in the new class provides a better fit than other generalized Weibull distributions.

scholarly journals The Exponentiated Generalized Topp Leone-G Family of Distributions: Properties and Applications

2019 ◽  
Vol 15 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Hesham Mohamed Reyad ◽  
Morad Alizadeh ◽  
Farrukh Jamal ◽  
Soha Othman ◽  
G G Hamedani
Keyword(s):  
Extreme Values ◽  
Residual Life ◽  
Information Matrix ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
New Class ◽  
New Family ◽  
Mathematical Properties

In this paper, we propose a new class of continuous distributions called the exponentiated generalized Topp Leone-G family that extends the Topp Leone-G family introduced by Al-Shomrani et al. (2016). We derive explicit expressions for certain mathematical properties of the new family such as; ordinary and incomplete moments, generating functions, reliability analysis, Lorenz and Bonferroni curves, Rényi entropy, stress strength model, moment of residual and reversed residual life, order statistics and extreme values. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the flexibility of the new family.

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.

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 On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

scholarly journals A Note on the Properties of Generalised Separable Spatial Autoregressive Process

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Mahendran Shitan ◽  
Shelton Peiris
Keyword(s):  
Three Dimensional ◽  
Real Data ◽  
Autoregressive Process ◽  
Spatial Modelling ◽  
Spectral Density Function ◽  
Data Sets ◽  
Additional Parameter ◽  
New Class ◽  
Spatial Autoregressive ◽  
Modelling And Forecasting

Spatial modelling has its applications in many fields like geology, agriculture, meteorology, geography, and so forth. In time series a class of models known as Generalised Autoregressive (GAR) has been introduced by Peiris (2003) that includes an index parameterδ. It has been shown that the inclusion of this additional parameter aids in modelling and forecasting many real data sets. This paper studies the properties of a new class of spatial autoregressive process of order 1 with an index. We will call this aGeneralised Separable Spatial Autoregressive(GENSSAR) Model. The spectral density function (SDF), the autocovariance function (ACVF), and the autocorrelation function (ACF) are derived. The theoretical ACF and SDF plots are presented as three-dimensional figures.

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