Applications of Truncated Cauchy Power Log-Logistic Model to Physical and Biomedical Data

2020 ◽  
Vol 12 (1) ◽  
pp. 25-33
Author(s):  
Majdah M. Badr
Keyword(s):  
Logistic Model ◽  
Maximum Likelihood Method ◽  
Numerical Study ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Biomedical Data ◽  
Proposed Model ◽  
Lifetime Model

In this article, we introduce a new three-parameter lifetime model, which is called truncated Cauchy power Log-Logistic (TCPLL) model. The TCPLL model has many applications in different sciences, such as physics and medicine, and we show that in the application section. We used two real-life datasets related to physics and medicine to show the flexibility of the TCPLL model. The TCPLL distribution is more flexible than some well-known models. The TCPLL parameters are estimated using maximum likelihood method for estimation. The numerical study is displayed to show the effectiveness of the estimates. At the end, we calculated some important properties like, quantile function, moments, order statistics and moment generating function of the proposed model.

scholarly journals Alpha Power Transformed Log-Logistic Distribution with Application to Breaking Stress Data

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Maha A. Aldahlan
Keyword(s):  
Maximum Likelihood Method ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Alpha Power ◽  
New Model ◽  
Mathematical Properties

In this paper, a new three-parameter lifetime distribution is introduced; the new model is a generalization of the log-logistic (LL) model, and it is called the alpha power transformed log-logistic (APTLL) distribution. The APTLL distribution is more flexible than some generalizations of log-logistic distribution. We derived some mathematical properties including moments, moment-generating function, quantile function, Rényi entropy, and order statistics of the new model. The model parameters are estimated using maximum likelihood method of estimation. The simulation study is performed to investigate the effectiveness of the estimates. Finally, we used one real-life dataset to show the flexibility of the APTLL distribution.

Truncated Cauchy Power Lomax Model and Its Application to Biomedical Data

2020 ◽  
Vol 12 (1) ◽  
pp. 16-24
Author(s):  
Abdullah M. Almarashi
Keyword(s):  
Maximum Likelihood Method ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Biomedical Data ◽  
Physical Sciences ◽  
Cancer Dataset ◽  
Fundamental Properties ◽  
New Distribution

In this study, we propose a new lifetime model, named truncated Cauchy power Lomax (TCPL) distribution. The TCPL distribution has many applications in biomedical and physical sciences, and we illustrate that its application herein. We used bladder cancer dataset related to medicine to illustrate the flexibility of the TCPL distribution. The new distribution is more flexible than some well-known models. We also calculated some fundamental properties like; moments, quantile function, moment generating function and order statistics for the TCPL model. The model parameters were estimated using maximum likelihood method for estimation. At the end of the paper, the simulation study is performed to assess the effectiveness of the estimates.

scholarly journals THE TRANSMUTED GAMMA-GOMPERTZ DISTRIBUTION

2020 ◽  
Vol 8 (10) ◽  
pp. 236-248
Author(s):  
Rwabi AzZwideen ◽  
Loai M. Al Zou’bi
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Generating Function ◽  
Maximum Likelihood Method ◽  
Probability Model ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Gompertz Distribution ◽  
Proposed Model

This article introduces a four-parameter probability model which represents a gener- alization of the the Gamma-Gompertz distribution using the quadratic rank trans- mutation map. The proposed model is named the Transmuted Gamma-Gompertz distribution. We provide explicit expressions for its statistical properties, moment generating function, quantile function, the order statistics, the quantile function and the median. We estimate the parameters of the distribution using the maximum likelihood method of estimation.

scholarly journals Sine Half-Logistic Inverse Rayleigh Distribution: Properties, Estimation, and Applications in Biomedical Data

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
M. Shrahili ◽  
I. Elbatal ◽  
Mohammed Elgarhy
Keyword(s):  
Maximum Likelihood Method ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Biomedical Data ◽  
Type Ii ◽  
Entropy Measures ◽  
Distribution Parameters ◽  
Two Parameters

A new lifetime distribution with two parameters, known as the sine half-logistic inverse Rayleigh distribution, is proposed and studied as an extension of the half-logistic inverse Rayleigh model. The sine half-logistic inverse Rayleigh model is a new inverse Rayleigh distribution extension. In the application section, we show that the sine half-logistic inverse Rayleigh distribution is more flexible than the half-logistic inverse Rayleigh and inverse Rayleigh distributions. The statistical properties of the half-logistic inverse Rayleigh model are calculated, including the quantile function, moments, moment generating function, incomplete moment, and Lorenz and Bonferroni curves. Entropy measures such as Rényi entropy, Havrda and Charvat entropy, Arimoto entropy, and Tsallis entropy are proposed for the sine half-logistic inverse Rayleigh distribution. To estimate the sine half-logistic inverse Rayleigh distribution parameters, statistical inference using the maximum likelihood method is used. Applications of the sine half-logistic inverse Rayleigh model to real datasets demonstrate the flexibility of the sine half-logistic inverse Rayleigh distribution by comparing it to well-known models such as half-logistic inverse Rayleigh, type II Topp–Leone inverse Rayleigh, transmuted inverse Rayleigh, and inverse Rayleigh distributions.

scholarly journals A New Generalized Transmuted Inverse Exponential Distribution: Properties and Application

2018 ◽  
pp. 1-13
Author(s):  
Uchenna U. Uwadi ◽  
Elebe E. Nwaezza
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Real Life Data ◽  
Proposed Model ◽  
Inverse Exponential Distribution ◽  
The Moment

In this study, we proposed a new generalised transmuted inverse exponential distribution with three parameters and have transmuted inverse exponential and inverse exponential distributions as sub models. The hazard function of the distribution is nonmonotonic, unimodal and inverted bathtub shaped making it suitable for modelling lifetime data. We derived the moment, moment generating function, quantile function, maximum likelihood estimates of the parameters, Renyi entropy and order statistics of the distribution. A real life data set is used to illustrate the usefulness of the proposed model.     

scholarly journals A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

MATHEMATICAL PROPERTIES AND APPLICATIONS OF MINIMUM GUMBEL BURR DISTRIBUTION

2020 ◽  
Vol XVII (2) ◽  
pp. 1-14
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Syed Muhammad Akbar Ali Shah
Keyword(s):  
Stochastic Ordering ◽  
Quantile Function ◽  
Continuous Model ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Parameter Estimates ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Burr Distribution ◽  
New Distribution

This paper presents the details of a proposed continuous model for the minimum Gumbel Burr distribution which is based on four different parameters. The model is obtained by compounding the Gumbel type-II and Burr-XII distributions. Basic mathematical properties of the new distribution were studied including the quantile function, ordinary and incomplete moments, moment generating function, order statistics, Rényi entropy, stress-strength model and stochastic ordering. The parameters of the proposed distribution are estimated using the maximum likelihood method. A Monte Carlo simulation was presented to examine the behaviour of the parameter estimates. The flexibility of the proposed model was assessed by means of three applications.

scholarly journals Some Properties and Applications of Topp Leone Kumaraswamy Lomax Distribution

2021 ◽  
Vol 3 (2) ◽  
pp. 81-94
Author(s):  
Sule Ibrahim ◽  
Sani Ibrahim Doguwa ◽  
Audu Isah ◽  
Haruna, M. Jibril
Keyword(s):  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Data Sets ◽  
Lifetime Distributions ◽  
Air Conditioning System ◽  
Lomax Distribution ◽  
Real Life Data ◽  
New Distribution

Many Statisticians have developed and proposed new distributions by extending the existing distributions. The distributions are extended by adding one or more parameters to the baseline distributions to make it more flexible in fitting different kinds of data. In this study, a new four-parameter lifetime distribution called the Topp Leone Kumaraswamy Lomax distribution was introduced by using a family of distributions which has been proposed in the literature. Some mathematical properties of the distribution such as the moments, moment generating function, quantile function, survival, hazard, reversed hazard and odds functions were presented. The estimation of the parameters by maximum likelihood method was discussed. Three real life data sets representing the failure times of the air conditioning system of an air plane, the remission times (in months) of a random sample of one hundred and twenty-eight (128) bladder cancer patients and Alumina (Al2O3) data were used to show the fit and flexibility of the new distribution over some lifetime distributions in literature. The results showed that the new distribution fits better in the three datasets considered.

The shifted Gompertz-G family of distributions: Properties and applications

2021 ◽  
Vol 71 (5) ◽  
pp. 1291-1308
Author(s):  
Joseph Thomas Eghwerido ◽  
Friday Ikechukwu Agu
Keyword(s):  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Real Life ◽  
Likelihood Method ◽  
Test Statistic ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Proposed Model ◽  
Left And Right ◽  
Mean Variance

Abstract This article proposes a class of generator for classical statistical distribution called the shifted Gompertz-G (SHIGO-G) distribution for generating new continuous distributions. Special models of the proposed model were examined together with some of its statistical properties in closed form which makes it tractable for censored data. Its major properties include heavy tail, approximately symmetric, left and right skewed with a combination of exponential and a reverted Gumbel distributions called the Gompertz. The bivariate SHIGO-G is introduced. The parameters estimate of the proposed model was obtained by maximum likelihood method. A Monte Carlo simulation study was employed to investigate the performance of the estimators of the proposed model mean, variance, bias and mean square error. A two real life illustration was used to examine the empirical goodness-of-fit of the test statistic of the proposed model. The results of the real life applications show that the SHIGO-G model provides a better fit for the data set used.

scholarly journals The Modified Beta Gompertz Distribution: Theory and Applications

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 3
Author(s):  
Ibrahim Elbatal ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy ◽  
Sharifah Alrajhi
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Simulation Study ◽  
Maximum Likelihood Method ◽  
Maximum Likelihood Estimators ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Gompertz Distribution

In this paper, we introduce a new continuous probability distribution with five parameters called the modified beta Gompertz distribution. It is derived from the modified beta generator proposed by Nadarajah, Teimouri and Shih (2014) and the Gompertz distribution. By investigating its mathematical and practical aspects, we prove that it is quite flexible and can be used effectively in modeling a wide variety of real phenomena. Among others, we provide useful expansions of crucial functions, quantile function, moments, incomplete moments, moment generating function, entropies and order statistics. We explore the estimation of the model parameters by the obtained maximum likelihood method. We also present a simulation study testing the validity of maximum likelihood estimators. Finally, we illustrate the flexibility of the distribution by the consideration of two real datasets.

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