scholarly journals A New Odd Lindley-Gompertz Distribution: Its Properties and Applications

2020 ◽  
pp. 29-47
Author(s):  
Omolola Dorcas Atanda ◽  
Tajan Mashingil Mabur ◽  
Gerald Ikechukwu Onwuka
Keyword(s):  
Generating Function ◽  
Hazard Function ◽  
Goodness Of Fit ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Reliability Function ◽  
Moment Generating Function ◽  
Gompertz Distribution ◽  
Better Than

This article presents a comprehensive study of an odd Lindley-Gompertz distribution which has already been proposed in the literature but without any properties. The present study unlike the previous one has considered the derivation of several properties of the odd Lindley-Gompertz distribution with their graphical representations and discussions which has not been done in the first proposition of the distribution.  The study looks at properties such as survival (or reliability) function, the hazard function, the cumulative hazard function, the reverse hazard function, the odds function, quantile function, moments, moment generating function, characteristic function, cumulant generating function, distribution of order statistics and maximum likelihood estimation of the distribution’s parameters none of which was treated by the previous author of the model. An illustration to evaluate the goodness-of-fit of the odd Lindley-Gompertz distribution has also been done using two real life datasets and the results show that the model fits the datasets better than the five other distributions considered in this present study.

Mathematical properties of the Kumaraswamy-Lindley distribution and its applications

2017 ◽  
Vol 5 (1) ◽  
pp. 17
Author(s):  
Hamdy Salem ◽  
Abd-Elwahab Hagag
Keyword(s):  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Least Square ◽  
Estimation Of Parameters ◽  
Least Square Estimation ◽  
Mathematical Properties ◽  
Composite Distribution

In this paper, a composite distribution of Kumaraswamy and Lindley distributions namely, Kumaraswamy-Lindley Kum-L distribution is introduced and studied. The Kum-L distribution generalizes sub-models for some widely known distributions. Some mathematical properties of the Kum-L such as hazard function, quantile function, moments, moment generating function and order statistics are obtained. Estimation of parameters for the Kum-L using maximum likelihood estimation and least square estimation techniques are provided. To illustrate the usefulness of the proposed distribution, simulation study and real data example are used.

scholarly journals A New Generalization of the Generalized Inverse Rayleigh Distribution with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 711
Author(s):  
Rana Ali Bakoban ◽  
Ashwaq Mohammad Al-Shehri
Keyword(s):  
Generalized Inverse ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Reliability Function ◽  
Rayleigh Distribution ◽  
Information Criteria ◽  
Difference Fields ◽  
The Mean

In this article, a new four-parameter lifetime model called the beta generalized inverse Rayleigh distribution (BGIRD) is defined and studied. Mixture representation of this model is derived. Curve’s behavior of probability density function, reliability function, and hazard function are studied. Next, we derived the quantile function, median, mode, moments, harmonic mean, skewness, and kurtosis. In addition, the order statistics and the mean deviations about the mean and median are found. Other important properties including entropy (Rényi and Shannon), which is a measure of the uncertainty for this distribution, are also investigated. Maximum likelihood estimation is adopted to the model. A simulation study is conducted to estimate the parameters. Four real-life data sets from difference fields were applied on this model. In addition, a comparison between the new model and some competitive models is done via information criteria. Our model shows the best fitting for the real data.

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 A generalization to the log-inverse Weibull distribution and its applications in cancer research

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
C. Satheesh Kumar ◽  
Subha R. Nair
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Life ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Reliability Function ◽  
Rate Function ◽  
Data Sets ◽  
Inverse Weibull Distribution

AbstractIn this paper we consider a generalization of a log-transformed version of the inverse Weibull distribution. Several theoretical properties of the distribution are studied in detail including expressions for its probability density function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, percentile measures, entropy measures, median, mode etc. Certain structural properties of the distribution along with expressions for reliability measures as well as the distribution and moments of order statistics are obtained. Also we discuss the maximum likelihood estimation of the parameters of the proposed distribution and illustrate the usefulness of the model through real life examples. In addition, the asymptotic behaviour of the maximum likelihood estimators are examined with the help of simulated data sets.

scholarly journals Odd Lindley-Kumaraswamy Distribution: Model, Properties and Application

2020 ◽  
pp. 42-58
Author(s):  
Kuje Samson ◽  
Abubakar, Mohammad Auwal ◽  
Asongo, Iorkaa Abraham ◽  
Alhaji, Ismaila Sulaiman
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Distribution Model ◽  
Model Parameters ◽  
Kumaraswamy Distribution ◽  
Method Of Maximum Likelihood ◽  
Compound Distribution

This article uses the odd Lindley-G family of distributions to propose and study a new compound distribution called “odd Lindley-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lindley-Kumaraswamy distribution are defined and studied by deriving and discussing many properties of the distribution such as the ordinary moments, moment generating function, characteristics function, quantile function, reliability functions, order statistics and other useful measures. The unknown model parameters are also estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real life datasets. The results show that the proposed distribution outperforms the other fitted compound models selected for this study and hence it is a flexible generalization of the Kumaraswamy distribution.

scholarly journals Properties and Applications of a Transmuted Power Gompertz Distribution

2020 ◽  
pp. 41-58
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Adana’a Felix Chama ◽  
Abraham Iorkaa Asongo ◽  
Bassa Shiwaye Yakura ◽  
Abdul Haruna Bala
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Maximum Likelihood Estimation ◽  
Goodness Of Fit ◽  
Real Life ◽  
Likelihood Estimation ◽  
New Model ◽  
Gompertz Distribution ◽  
Method Of Maximum Likelihood ◽  
Result Show

This article introduces and studies a new probability distribution called “Transmuted Power Gompertz distribution”. It looks at the properties of the transmuted power Gompertz distribution. The article also estimates the four parameters of the new model using the method of maximum likelihood estimation. The article further evaluates the goodness-of-fit of the proposed distribution compared to other distributions by means of applications of the model to two real life datasets and the result show that the proposed distribution is more flexible than the fitted existing distributions.

scholarly journals On Properties and Applications of Lomax-Gompertz Distribution

2019 ◽  
pp. 1-17
Author(s):  
A. Omale ◽  
O. E. Asiribo ◽  
A. Yahaya
Keyword(s):  
Survival Function ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Gompertz Distribution ◽  
Probability Of Survival ◽  
Method Of Maximum Likelihood ◽  
Age Dependent ◽  
New Distribution

This article introduces a new distribution called the Lomax-Gompertz distribution developed through a Lomax Generator proposed in an earlier study. Some statistical properties of the proposed distribution comprising moments, moment generating function, characteristics function, quantile function and the distribution of order statistics were derived. The plots of the probability density function revealed that it is positively skewed. The model parameters have been estimated using the method of maximum likelihood. The plot the of survival function indicates that the Lomax-Gompertz distribution could be used to model time or age-dependent data, where probability of survival is believed to be  decreasing  with time or age. The performance of the Lomax-Gompertz distribution has been compared to other generalizations of the Gompertz distribution using three real-life datasets used in earlier researches.

scholarly journals Exponentiated Cubic Transmuted Weibull Distribution: Properties and Application

2021 ◽  
pp. 1-11
Author(s):  
Oseghale O. I. ◽  
Akomolafe A. A. ◽  
Gayawan E.
Keyword(s):  
Weibull Distribution ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Estimation Technique ◽  
Life Data ◽  
Real Life Data

This work is focused on the four parameters Exponentiated Cubic Transmuted Weibull distribution which mostly found its application in reliability analysis most especially for data that are non-monotone and Bi-modal. Structural properties such as moment, moment generating function, Quantile function, Renyi entropy, and order statistics were investigated. The maximum likelihood estimation technique was used to estimate the parameters of the distribution. Application to two real-life data sets shows the applicability of the distribution in modeling real data.

scholarly journals An Extended Pranav Distribution

2019 ◽  
pp. 1-15
Author(s):  
O. R. Uwaeme ◽  
N. P. Akpan ◽  
U. C. Orumie
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Reliability Function ◽  
Moment Generating Function ◽  
Cumulative Distribution ◽  
Maximum Likelihood Estimates ◽  
Statistical Characteristics ◽  
Data Sets ◽  
Rate Functions ◽  
New Distribution

In this study, we proposed a generalization of the Pranav distribution by Shukla (2018). This new distribution called an extended Pranav distribution is obtained using the exponentiation method. The statistical characteristics of this new distribution such as the moments, moment generating function, reliability function, hazard function, Rényi entropy and order statistics are derived. The graphical illustrations of the shapes of the probability density function, the cumulative distribution function, and hazard rate functions are provided. The maximum likelihood estimates of the parameters were obtained and finally, we examine the performance of this new distribution using some real-life data sets to show its flexibility and better goodness of fit as compared with other distributions.

scholarly journals The Zubair-dagum Distribution

2021 ◽  
pp. 25-35
Author(s):  
O. R. Uwaeme ◽  
N. P. Akpan
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Parameter Estimates ◽  
Mathematical Properties ◽  
Dagum Distribution ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This article examines the flexibility of the Zubair-G family of distribution using the Dagum distribution. The proposed distribution is called the Zubair-Dagum distribution. The various mathematical properties of this distribution such as the Quantile function, Moments, Moment generating function, Reliability analysis, Entropy and Order statistics were obtained. The parameter estimates of the proposed distribution were also derived and estimated using the maximum likelihood estimation method. The new distribution is right skewed and has various bathtub and monotonically decreasing shapes. Our numerical illustrations using two real-life datasets substantiate the applicability, flexibility and superiority of the proposed distribution over competing distributions.

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