scholarly journals Bivariate Transmuted Burr Distribution: Properties and Application

2021 ◽  
pp. 15-24
Author(s):  
Muhammad Qaiser Shahbaz ◽  
Jumanah Ahmed Darwish ◽  
Lutfiah Ismail Al Turk
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Bivariate Distribution ◽  
Conditional Distributions ◽  
Conditional Moments ◽  
Data Application ◽  
Burr Distribution ◽  
Rate Functions ◽  
Simultaneous Modeling ◽  
Complex Joint

The bivariate distributions are useful in simultaneous modeling of two random variables. These distributions provide a way of modeling complex joint phenomenon. In this article, a new bivariate distribution is proposed which is known as the bivariate transmuted Burr (BTB) distribution. This new bivariate distribution is extension of the univariate transmuted Burr (TB) distribution to two variables. The proposed  BTB distribution is explored in detail and the marginal and conditional distributions for the distribution are obtained. Joint and conditional moments alongside hazard rate functions are obtained. The maximum likelihood estimation (MLE) for the parameters of the BTB distribution is also done. Finally, real data application of the BTB distribution is given. It is observed that the proposed BTB distribution is a suitable fit for the data used.

scholarly journals Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2164
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Karol I. Santoro
Keyword(s):  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
R Software ◽  
Data Application ◽  
The Em Algorithm ◽  
Kurtosis Parameter ◽  
Computational Implementation ◽  
Moments Method

In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominator). The resulting model has greater kurtosis than the TPN distribution. We studied some properties of the distribution, such as moments, asymmetry, and kurtosis. Parameter estimation is based on the moments method, and maximum likelihood estimation uses the expectation-maximization algorithm. We performed some simulation studies to assess the recovery parameters and illustrate the model with a real data application related to body weight. The computational implementation of this work was included in the tpn package of the R software.

scholarly journals A Mixture of Inverse Weibull and Inverse Burr Distributions: Properties, Estimation, and Fitting

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
A. S. Al-Moisheer ◽  
K. S. Sultan ◽  
M. A. Al-Shehri
Keyword(s):  
Mixture Model ◽  
Classical Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Probability Density Functions ◽  
Density Functions ◽  
Data Set ◽  
Burr Distributions ◽  
Lindley’S Approximation ◽  
Rate Functions

The new mixture model of the two components of the inverse Weibull and inverse Burr distributions (MIWIBD) is proposed. First, the properties of the investigated mixture model are introduced and the behaviors of the probability density functions and hazard rate functions are displayed. Then, the estimates of the five-dimensional vector of parameters by using the classical method such as the maximum likelihood estimation (MLEs) and the approximation method by using Lindley’s approximation are obtained. Finally, a real data set for the proposed mixture model is applied to illustrate the proposed mixture model.

scholarly journals A New Burr XII-Weibull-Logarithmic Distribution for Survival and Lifetime Data Analysis: Model, Theory and Applications

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 77-91
Author(s):  
Broderick Oluyede ◽  
Boikanyo Makubate ◽  
Adeniyi Fagbamigbe ◽  
Precious Mdlongwa
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Analysis Model ◽  
Conditional Moments ◽  
Compound Distribution ◽  
Lifetime Data Analysis ◽  
Logarithmic Distribution ◽  
New Distribution

A new compound distribution called Burr XII-Weibull-Logarithmic (BWL) distribution is introduced and its properties are explored. This new distribution contains several new and well known sub-models, including Burr XII-Exponential-Logarithmic, Burr XII-Rayleigh-Logarithmic, Burr XII-Logarithmic, Lomax-Exponential-Logarithmic, Lomax–Rayleigh-Logarithmic, Weibull, Rayleigh, Lomax, Lomax-Logarithmic, Weibull-Logarithmic, Rayleigh-Logarithmic, and Exponential-Logarithmic distributions. Some statistical properties of the proposed distribution including moments and conditional moments are presented. Maximum likelihood estimation technique is used to estimate the model parameters. Finally, applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.

scholarly journals Mixture of Lindley and Inverse Weibull Distributions: Properties and Estimation

2021 ◽  
Vol 20 ◽  
pp. 134-143
Author(s):  
A. S. Al-Moisheer ◽  
A. F. Daghestani ◽  
K. S. Sultan
Keyword(s):  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Real Data ◽  
Estimation Methods ◽  
Simulation Studies ◽  
Weibull Distributions ◽  
Unknown Parameters ◽  
Data Application ◽  
Rate Functions ◽  
And Behavior

In this paper, we talk about a mixture of one-parameter Lindley and inverse Weibull distributions (MLIWD). First, We introduce and discuss the MLIWD. Then, we study the main statistical properties of the proposed mixture and provide some graphs of both the density and the associated hazard rate functions. After that, we estimate the unknown parameters of the proposed mixture via two estimation methods, namely, the generalized method of moments and maximum likelihood. In addition, we compare the estimation methods via some simulation studies to determine the efficacy of the two estimation methods. Finally, we evaluate the performance and behavior of the proposed mixture with different numerical examples and real data application in survival analysis.

scholarly journals Insurance ratemaking using the Exponential-Lognormal regression model

2019 ◽  
Vol 14 (1) ◽  
pp. 42-71
Author(s):  
George Tzougas ◽  
Woo Hee Yik ◽  
Muhammad Waqar Mustaqeem
Keyword(s):  
Regression Model ◽  
Negative Binomial ◽  
A Priori ◽  
Likelihood Estimation ◽  
Real Data ◽  
Inverse Gamma ◽  
Data Application ◽  
Expectation Maximisation ◽  
Wide Range ◽  
Gaussian Regression

AbstractThis paper is concerned with presenting the Exponential-Lognormal (ELN) regression model as a competitive alternative to the Pareto, or Exponential-Inverse Gamma, regression model that has been used in a wide range of areas, including insurance ratemaking. This is the first time that the ELN regression model is used in a statistical or actuarial context. The main contribution of the study is that we illustrate how maximum likelihood estimation of the ELN regression model, which does not have a density in closed form, can be accomplished relatively easily via an Expectation-Maximisation type algorithm. A real data application based on motor insurance data is examined in order to emphasise the versatility of the proposed algorithm. Finally, assuming that the number of claims is distributed according to the classic Negative Binomial and Poisson-Inverse Gaussian regression models, both the a priori and a posteriori, or Bonus–Malus, premium rates resulting from the ELN regression model are calculated via the net premium principle and compared to those determined by the Pareto regression model that has been traditionally used for modelling claim sizes.

scholarly journals On The Burr XII-Gamma Distribution: Development, Properties, Characterizations and Applications

2021 ◽  
pp. 771-789
Author(s):  
Fiaz Ahmad Bhatti ◽  
Gauss M. Cordeiro ◽  
Mustafa Ç. Korkmaz ◽  
G.G. Hamedani
Keyword(s):  
Random Number Generator ◽  
Likelihood Estimation ◽  
Real Data ◽  
Record Values ◽  
Rate Function ◽  
Data Sets ◽  
Failure Rate Function ◽  
Conditional Moments ◽  
Mathematical Properties ◽  
Proposed Model

We introduce a four-parameter lifetime model with flexible hazard rate called the Burr XII gamma (BXIIG) distribution.  We derive the BXIIG distribution from (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The failure rate function for the BXIIG distribution is flexible as it can accommodate various shapes such as increasing, decreasing, decreasing-increasing, increasing-decreasing-increasing, bathtub and modified bathtub.  Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXIIG distribution, we establish various mathematical properties such as random number generator, ordinary moments, generating function, conditional moments, density functions of record values, reliability measures and characterizations.  We address the maximum likelihood estimation for the parameters. We estimate the adequacy of the estimators via a simulation study. We consider applications to two real data sets to prove empirically the potentiality of the proposed model.

scholarly journals Some Cubic Rank Transmuted Distributions

2018 ◽  
Vol 14 (2) ◽  
pp. 27-43
Author(s):  
Nuri Celik
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Probability Density Functions ◽  
Density Functions ◽  
Rate Functions ◽  
Maximum Likelihood Estimation Method ◽  
Parameters Of Interest

Abstract In this article, we introduce some examples of cubic rank transmuted distributions proposed by Granzatto et al. (2017). The statistical aspects of the introduced distributions such as probability density functions, hazard rate functions and reliability functions are studied. The maximum likelihood estimation method is used in order to estimate the parameters of interest. Finally, real data examples are applied for the illustration of these distributions.

scholarly journals A New Lindley-Burr XII Distribution: Model, Properties and Applications

2021 ◽  
Vol 10 (4) ◽  
pp. 33
Author(s):  
Boikanyo Makubate ◽  
Broderick Oluyede ◽  
Morongwa Gabanakgosi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Distribution Model ◽  
Model Parameters ◽  
Data Sets ◽  
Mean Square ◽  
Conditional Moments ◽  
New Distribution

A new distribution called the Lindley-Burr XII (LBXII) distribution is proposed and studied. Some structural properties of the new distribution including moments, conditional moments, distribution of the order statistics and R´enyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and applications to real data sets in order to illustrate the usefulness of the new distribution are given.

scholarly journals Bivariate Compound Exponentiated Survival Function of the Lomax Distribution: Estimation and Prediction

2021 ◽  
pp. 163-184
Author(s):  
R. M. Refaey ◽  
G. R. AL-Dayian ◽  
A. A. EL-Helbawy ◽  
A. A. EL-Helbawy
Keyword(s):  
Survival Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Bivariate Distribution ◽  
Data Set ◽  
Squared Error Loss Function ◽  
Lomax Distribution ◽  
Estimation And Prediction ◽  
Squared Error

In this paper, bivariate compound exponentiated survival function of the Lomax distribution is constructed based on the technique considered by AL-Hussaini (2011). Some properties of the distribution are derived. Maximum likelihood estimation and prediction of the future observations are considered. Also, Bayesian estimation and prediction are studied under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a real data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

scholarly journals An Estimation of Survival and Hazard Rate Functions of Exponential Rayleigh Distribution

2021 ◽  
Vol 34 (4) ◽  
pp. 93-107
Author(s):  
Lamyaa Khalid Hussein ◽  
Iden Hasan Hussein ◽  
Huda Abdulla Rasheed
Keyword(s):  
Lung Cancer ◽  
Maximum Likelihood ◽  
Hazard Rate ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Medical City ◽  
Rate Functions ◽  
Maximum Likelihood Estimation Method

In this paper, we used the maximum likelihood estimation method to find the estimation values ​​for survival and hazard rate functions of the Exponential Rayleigh distribution based on a sample of the real data for lung cancer and stomach cancer obtained from the Iraqi Ministry of Health and Environment, Department of Medical City, Tumor Teaching Hospital, depending on patients' diagnosis records and number of days the patient remains in the hospital until his death.

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