scholarly journals A Weibull-Gompertz Makeham Distribution with Properties and Application to Cancer Data

2019 ◽  
pp. 1-17
Author(s):  
Peter O. Koleoso ◽  
Angela U. Chukwu
Keyword(s):  
Bladder Cancer ◽  
Maximum Likelihood ◽  
Order Statistics ◽  
Hazard Function ◽  
Probability Distributions ◽  
Survival Function ◽  
Statistical Properties ◽  
Cancer Data ◽  
Method Of Maximum Likelihood ◽  
Flexible Model

The article presents an extension of the Gompertz Makeham distribution using the Weibull-G family of continuous probability distributions proposed by Tahir et al. (2016a). This new extension generates a more flexible model called Weibull-Gompertz Makeham distribution. Some statistical properties of the distribution which include the moments, survival function, hazard function and distribution of order statistics were derived and discussed. The parameters were estimated by the method of maximum likelihood and the distribution was applied to a bladder cancer data. Weibull-Gompertz Makeham distribution performed best (AIC = -6.8677, CAIC = -6.3759, BIC = 7.3924) when compared with other existing distributions of the same family to model bladder cancer data.

scholarly journals The Exponentiated Generalized-G Poisson Family of Distributions

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Gokarna R. Aryal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Real World ◽  
Generating Functions ◽  
Real World Data ◽  
New Family ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

AbstractIn this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.

scholarly journals The Equilibrium Renewal Burr XII Distribution: Properties and Applications

2021 ◽  
pp. 18-40
Author(s):  
Abdulzeid Yen Anafo ◽  
Lewis Brew ◽  
Suleman Nasiru
Keyword(s):  
Probability Distribution ◽  
Hazard Rate ◽  
Lorenz Curve ◽  
Hazard Function ◽  
Survival Function ◽  
Moment Generating Function ◽  
Mean Deviation ◽  
Reversed Hazard Rate ◽  
Burr Xii Distribution ◽  
Method Of Maximum Likelihood

In this paper, we propose a three-parameter probability distribution called equilibrium renewal Burr XII distribution using the equilibrium renewal process. The statistical properties of the distribution such as moment, mean deviation, order statistics, moment generating function, Beforroni and Lorenz curve, survival function, reversed hazard rate and hazard function were derived. The method of maximum likelihood is used for estimating the distribution's parameters and a simulation study is conducted to assess the performance of the parameters. We provide two applications in eld of health to demonstrate the importance of the proposed distribution.

scholarly journals On modified Kies distribution and its applications

2017 ◽  
Vol 51 (1) ◽  
pp. 41-60
Author(s):  
C. SATHEESH KUMAR ◽  
S. H. S. DHARMAJA
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Real Life ◽  
Simulated Data ◽  
Maximum Likelihood Estimators ◽  
Data Sets ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Simulated Data Sets

In this paper, we consider a class of bathtub-shaped hazard function distribution through modifying the Kies distribution and investigate some of its important properties by deriving expressions for its percentile function, raw moments, stress-strength reliability measure etc. The parameters of the distribution are estimated by the method of maximum likelihood and discussed some of its reliability applications with the help of certain real life data sets. In addition, the asymptotic behavior of the maximum likelihood estimators of the parameters of the distribution is examined by using simulated data sets.

scholarly journals A Study on Properties and Applications of a Lomax Gompertz-Makeham Distribution

2019 ◽  
pp. 1-27
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Terna Godfrey Ieren ◽  
Tajan Mashingil Mabur ◽  
Mohammed Sa’ad ◽  
Samson Kuje ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Estimation ◽  
The Other ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Compound Model ◽  
New Distribution

The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.

scholarly journals A New One-parameter G Family of Compound Distributions: Copulas, Statistical Properties and Applications

2021 ◽  
Vol 9 (4) ◽  
pp. 942-962
Author(s):  
Mohamed Abo Raya
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Heavy Tail ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
New Family

This work introduces a new one-parameter compound G family. Relevant statistical properties are derived. The new density can be “asymmetric right skewed with one peak and a heavy tail”, “symmetric” and “left skewedwith one peak”. The new hazard function can be “upside-down”, “upside-down-constant”, “increasing”, “decreasing” and “decreasing-constant”. Many bivariate types have been also derived via different common copulas. The estimation of the model parameters is performed by maximum likelihood method. The usefulness and flexibility of the new family is illustrated by means of two real data sets.

scholarly journals On some properties of Generalized Transmuted Kumaraswamy distribution

2019 ◽  
pp. 577-586
Author(s):  
Aliyu Ismail Ishaq ◽  
Abubakar Usman ◽  
Tasiu Musa ◽  
Samson Agboola
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Survival Functions ◽  
Kumaraswamy Distribution ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
Lifetime Model

ABSTRACTThis articles introduces a new lifetime model called the generalized transmuted Kumaraswamy distribution which extends the Kumaraswamy distribution from the family proposed by Nofal et al., (2017). We provide hazard and survival functions of the proposed distribution. The statistical properties of the proposed model are provided and the method of Maximum Likelihood Estimation (MLE) was proposed in estimating its parameters.

scholarly journals The recurrence relations of order statistics moments for power Lomax distribution

2018 ◽  
Vol 52 (1) ◽  
pp. 75-90
Author(s):  
DEVENDRA KUMAR ◽  
SANKU DEY ◽  
MAZEN NASSAR ◽  
PREETI YADAV
Keyword(s):  
Bladder Cancer ◽  
Order Statistics ◽  
Recurrence Relations ◽  
Sample Sizes ◽  
Double Product ◽  
Cancer Data ◽  
Lomax Distribution ◽  
The Mean ◽  
Mean Variance ◽  
Skewness And Kurtosis

The power Lomax distribution due to Rady et al. (2016) is an alternative to and provides better fits for bladder cancer data (Lee and Wang, 2003) than the Lomax, exponential Lo- max, Weibull Lomax, extended Poisson Lomax and beta Lomax distributions. Exact explicit expressions as well as recurrence relations for the single and double (product) moments have been derived from the power Lomax distribution. These recurrence relations enable computation of the mean, variance, skewness and kurtosis of all order statistics for all sample sizes in a simple and efficient manner. By using these relation, the mean, variance, skewness and kurtosis of order statistics for sample sizes up to 5 for various values of shape and scale parameters are tabulated. Finally, remission times (in months) of bladder cancer patients have been analyzed to show how the proposed relations work in practice.

scholarly journals Basic Equations and Computing Procedures for Frailty Modeling of Carcinogenesis: Application to Pancreatic Cancer Data

2013 ◽  
Vol 12 ◽  
pp. CIN.S8063 ◽  
Author(s):  
Tengiz Mdzinarishvili ◽  
Simon Sherman
Keyword(s):  
Pancreatic Cancer ◽  
At Risk ◽  
Hazard Function ◽  
Survival Function ◽  
Population Level ◽  
Time Shift ◽  
Cumulative Hazard ◽  
Cancer Data ◽  
Weibull Pdf ◽  
Basic Equations

Modeling of cancer hazards at age t deals with a dichotomous population, a small part of which (the fraction at risk) will get cancer, while the other part will not. Therefore, we conditioned the hazard function, h( t), the probability density function (pdf), f( t), and the survival function, S( t), on frailty α in individuals. Assuming α has the Bernoulli distribution, we obtained equations relating the unconditional (population level) hazard function, hU( t), cumulative hazard function, HU( t), and overall cumulative hazard, H0, with the h( t), f( t), and S( t) for individuals from the fraction at risk. Computing procedures for estimating h( t), f( t), and S( t) were developed and used to ft the pancreatic cancer data collected by SEER9 registries from 1975 through 2004 with the Weibull pdf suggested by the Armitage-Doll model. The parameters of the obtained excellent fit suggest that age of pancreatic cancer presentation has a time shift about 17 years and five mutations are needed for pancreatic cells to become malignant.

scholarly journals A DISCRETE ANALOGUE OF THE CONTINUOUS POWER LINDLEY DISTRIBUTION AND ITS APPLICATIONS

2018 ◽  
Vol 36 (3) ◽  
pp. 649 ◽  
Author(s):  
Ricardo Puziol OLIVEIRA ◽  
Josmar MAZUCHELI ◽  
Márcia Lorena Alves SANTOS ◽  
Kelly Vanessa Parede BARCO
Keyword(s):  
Maximum Likelihood ◽  
Probability Distributions ◽  
Survival Function ◽  
Continuous Distribution ◽  
Discrete Analogue ◽  
Discrete Models ◽  
Lindley Distribution ◽  
Power Lindley Distribution ◽  
Proposed Model ◽  
Continuous Power

Methods to generate a discrete analogue of a continuous distribution have been widely considered in recent decades. In general, the discretization procedure comprises in transform continuous attributes into discrete attributes generating new probability distributions that could be an alternative to the traditional  discrete models, such as Poisson and Binomial models, commonly used in analysis of count data. It also  avoids the use of continuous in the analysis of strictly discrete data. In this paper, using the discretization  method based on the survival function, it is introduced a discrete analogue of power Lindley distribution. Some mathematical properties are studied. The maximum likelihood theory is considered for estimation and asymptotic inference concerns. A simulation study is also carried out in order to evaluate some properties of the maximum likelihood estimators of the proposed model. The usefulness and accurate of the proposed model are evaluated using real datasets provided by the literature.

scholarly journals A Power Gompertz Distribution: Model, Properties and Application to Bladder Cancer Data

2019 ◽  
pp. 1-14
Author(s):  
Terna Godfrey Ieren ◽  
Felix M. Kromtit ◽  
Blessing Uke Agbor ◽  
Innocent Boyle Eraikhuemen ◽  
Peter Oluwaseun Koleoso
Keyword(s):  
Bladder Cancer ◽  
Real Life ◽  
Likelihood Estimation ◽  
Distribution Model ◽  
Power Transformation ◽  
Statistical Features ◽  
Cancer Data ◽  
Gompertz Distribution ◽  
Method Of Maximum Likelihood ◽  
Cure Fraction

This paper uses a power transformation approach to introduce a three-parameter probability distribution which gives another extension of the Gompertz distribution known as “Power Gompertz distribution”. The statistical features of the power Gompertz distribution are systematically derived and studied appropriately. The three parameters of the new model are being estimated using the method of maximum likelihood estimation. The proposed distribution has also been compared to the Gompertz distribution using a real life dataset and the result shows that the Power Gompertz distribution has better performance than the Gompertz distribution and hence will be more useful and effective if applied in some real life situations especially survival analysis and cure fraction modeling just like the conventional Gompertz distribution.

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