scholarly journals The beta compound Rayleigh distribution : Properties and applications

2017 ◽  
Vol 5 (1) ◽  
pp. 57
Author(s):  
Hesham Reyad ◽  
Soha Ibrahim
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Continuous Model ◽  
Rayleigh Distribution ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Record Statistics ◽  
Mean Variance ◽  
Compound Rayleigh Distribution

In this paper, we introduce a new four parameter continuous model, called the beta compound Rayleigh (BCR) distribution that extends the compound Rayleigh distribution. Basic properties of the proposed distribution such as; mean, variance, coefficient of variation, raw and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics are investigated. We obtain the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the usefulness of the new model.

scholarly journals The Kumaraswamy compound Rayleigh distribution : properties and estimation

2017 ◽  
Vol 5 (1) ◽  
pp. 36
Author(s):  
Hesham Reyad ◽  
Soha A. Othman ◽  
Adil M Younis ◽  
Ahmed M. Hashish
Keyword(s):  
Generating Functions ◽  
Quantile Function ◽  
Continuous Model ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Mathematical Properties ◽  
Record Statistics ◽  
Methods Of Moments ◽  
Mean Variance ◽  
Compound Rayleigh Distribution

We introduce a new four parameter continuous model, called the Kumaraswamy compound Rayleigh (KwCR) distribution that extends the compound Rayleigh distribution. We study some mathematical properties of this distribution such as; mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics. We consider the methods of moments and maximum likelihood for estimating the model parameters.

scholarly journals The Transmuted Odd Lindley-G Family of Distributions

2018 ◽  
pp. 1-25 ◽  
Author(s):  
Hesham Reyad ◽  
Farrukh Jamal ◽  
Soha Othman ◽  
G. G. Hamedani
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Strength Model ◽  
New Family ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Family Of Distributions

We propose a new generator of univariate continuous distributions with two extra parameters called the transmuted odd-Lindley generator which extends the odd Lindely-G family introduced by Gomes-Silva et al. [1]. Some mathematical properties of the new generator such as, the ordinary and incomplete moments, generating function, stress strength model, Rényi entropy, probability weighted moments and order statistics are investigated. Certain characterisations of the proposed family are estimated. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. The potentiality of the new family is illustrated by means of five applications to real data sets.  

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.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

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 Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

2021 ◽  
pp. 9-37
Author(s):  
Samuel U. Enogwe ◽  
Chisimkwuo John ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Bathtub Shape ◽  
Asymptotic Confidence Intervals

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

scholarly journals New extensions of Rayleigh distribution based on inverted-Weibull and Weibull distributions

2021 ◽  
Vol 11 (6) ◽  
pp. 5107
Author(s):  
Mahmoud M. Smadi ◽  
Mahmoud H. Alrefaei
Keyword(s):  
Communication Systems ◽  
Communication Theory ◽  
Random Number Generation ◽  
Real Data ◽  
Quantile Function ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Data Sets ◽  
Hazard Functions ◽  
Radar Images

The Rayleigh distribution was proposed in the fields of acoustics and optics by lord Rayleigh. It has wide applications in communication theory, such as description of instantaneous peak power of received radio signals, i.e. study of vibrations and waves. It has also been used for modeling of wave propagation, radiation, synthetic aperture radar images, and lifetime data in engineering and clinical studies. This work proposes two new extensions of the Rayleigh distribution, namely the Rayleigh inverted-Weibull (RIW) and the Rayleigh Weibull (RW) distributions. Several fundamental properties are derived in this study, these include reliability and hazard functions, moments, quantile function, random number generation, skewness, and kurtosis. The maximum likelihood estimators for the model parameters of the two proposed models are also derived along with the asymptotic confidence intervals. Two real data sets in communication systems and clinical trials are analyzed to illustrate the concept of the proposed extensions. The results demonstrated that the proposed extensions showed better fitting than other extensions and competing models.

scholarly journals Generalized Beta-Exponential Weibull Distribution and its Applications

2020 ◽  
Vol 24 (1) ◽  
pp. 1-33
Author(s):  
N. I. Badmus ◽  
◽  
Olanrewaju Faweya ◽  
K. A. Adeleke ◽  
◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Hazard Functions ◽  
Generalized Distributions

In this article, we investigate a distribution called the generalized beta-exponential Weibull distribution. Beta exponential x family of link function which is generated from family of generalized distributions is used in generating the new distribution. Its density and hazard functions have different shapes and contains special case of distributions that have been proposed in literature such as beta-Weibull, beta exponential, exponentiated-Weibull and exponentiated-exponential distribution. Various properties of the distribution were obtained namely; moments, generating function, Renyi entropy and quantile function. Estimation of model parameters through maximum likelihood estimation method and observed information matrix are derived. Thereafter, the proposed distribution is illustrated with applications to two different real data sets. Lastly, the distribution clearly shown that is better fitted to the two data sets than other distributions.

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 Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1114
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón ◽  
María Martínez-Guerra
Keyword(s):  
Power Distribution ◽  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Score Functions ◽  
New Family ◽  
Two Parameters ◽  
Family Of Distributions

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

Sign in / Sign up

Export Citation Format

Share Document