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 A Transmuted Lomax-Exponential Distribution: Properties and Applications

2019 ◽  
pp. 1-13
Author(s):  
S. Kuje ◽  
K. E. Lasisi
Keyword(s):  
Exponential Distribution ◽  
Probability Distributions ◽  
Survival Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Cumulative Distribution ◽  
Method Of Maximum Likelihood ◽  
New Distribution

In this article, the Quadratic rank transmutation map proposed and studied by Shaw and Buckley [1] is used to construct and study a new distribution called the transmuted Lomax-Exponential distribution (TLED) as an extension of the Lomax-Exponential distribution recently proposed by Ieren and Kuhe [2]. Using the transmutation map, we defined the probability density function and cumulative distribution function of the transmuted Lomax-Exponential distribution. Some properties of the new distribution such as moments, moment generating function, characteristics function, quantile function, survival function, hazard function and order statistics are also studied. The estimation of the distributions’ parameters has been done using the method of maximum likelihood estimation. The performance of the proposed probability distribution is being tested in comparison with some other generalizations of Exponential distribution using a real life dataset. The results obtained show that the TLED performs better than the other probability distributions.

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 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 Odd Lomax-Kumaraswamy Distribution: Its Properties and Applications

2020 ◽  
pp. 45-60
Author(s):  
Bassa Shiwaye Yakura ◽  
Ahmed Askira Sule ◽  
Mustapha Mohammed Dewu ◽  
Kabiru Ahmed Manju ◽  
Fadimatu Bawuro Mohammed
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Functions ◽  
Model Parameters ◽  
Data Sets ◽  
Kumaraswamy Distribution ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

This article uses the odd Lomax-G family of distributions to study a new extension of the Kumaraswamy distribution called “odd Lomax-Kumaraswamy distribution”. In this article, the density and distribution functions of the odd Lomax-Kumaraswamy distribution are defined and studied with many other properties of the distribution such as the ordinary moments, moment generating function, characteristic function, quantile function, reliability functions, order statistics and other useful measures. The model parameters are estimated by the method of maximum likelihood. The goodness-of-fit of the proposed distribution is demonstrated using two real data sets.

scholarly journals The Generalized Ampadu-G Family of Distributions: Properties, Applications and Characterizations

2020 ◽  
pp. 139-167
Author(s):  
Clement Boateng Ampadu ◽  
Abdulzeid Yen Anafo
Keyword(s):  
Weibull Distribution ◽  
Density Function ◽  
Survival Function ◽  
Real Life ◽  
Life Time ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Model Parameters ◽  
New Family ◽  
Family Of Distributions

This paper introduces a new class of distributions called the generalized Ampadu-G (GA-G for short) family of distributions, and with a certain restriction on the parameter space, the family is shown to be a life-time distribution. The shape of the density function and hazard rate function of the GA-G family is described analytically. When G follows the Weibull distribution, the generalized Ampadu-Weibull (GA-W for short) is presented along with its hazard and survival function. Several sub-models of the GA-W family are presented. The transformation technique is applied to this new family of distributions, and we obtain the quantile function of the new family. Power series representations for the cumulative distribution function (CDF) and probability density function (PDF) are also obtained. The rth non-central moments, moment generating function, and Renyi entropy associated with the new family of distributions are derived. Characterization theorems based on two truncated moments and conditional expectation are also presented. A simulation study is also conducted, and we find that using the method of maximum likelihood to estimate model parameters is adequate. The GA-W family of distributions is shown to be practically significant in modeling real life data, and is shown to be superior to some non-trivial generalizations of the Weibull distribution. A further development concludes the paper.

scholarly journals The Gompertz Gumbel II Distribution: Properties and Applications

2020 ◽  
pp. 1-15
Author(s):  
Adebisi Ade Ogunde ◽  
Gbenga Adelekan Olalude ◽  
Donatus Osaretin Omosigho
Keyword(s):  
Real Life ◽  
Stochastic Ordering ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Life Data ◽  
Real Life Data ◽  
Decreasing Failure Rate ◽  
New Distribution

In this paper we introduced Gompertz Gumbel II (GG II) distribution which generalizes the Gumbel II distribution. The new distribution is a flexible exponential type distribution which can be used in modeling real life data with varying degree of asymmetry. Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which sometimes characterised the real life data. Structural properties of the new distribution namely, density function, hazard function, moments, quantile function, moment generating function, orders statistics, Stochastic Ordering, Renyi entropy were obtained. For the main formulas related to our model, we present numerical studies that illustrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the GGTT model. Three life data sets were used for applications in order to illustrate the flexibility of the new model.

scholarly journals Inverted Power Rama Distribution with Applications to Life Time Data

2020 ◽  
pp. 1-21
Author(s):  
Chrisogonus K. Onyekwere ◽  
George A. Osuji ◽  
Samuel U. Enogwe
Keyword(s):  
Heavy Tails ◽  
Survival Function ◽  
Real Life ◽  
Stochastic Ordering ◽  
Life Time ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Statistical Characteristics ◽  
Entropy Measure ◽  
Time Data

In this paper, we introduced the Inverted Power Rama distribution as an extension of the Inverted Rama distribution. This new distribution is capable of modeling real life data with upside down bathtub shape and heavy tails. Mathematical and statistical characteristics such as the quantile function, mode, moments and moment generating function, entropy measure, stochastic ordering and distribution of order statistics have been derived. Furthermore, reliability measures like survival function, hazard function and odds function have been derived. The method of maximum likelihood was used for estimating the parameters of the distribution. To demonstrate the applicability of the distribution, a numerical example was given. Based on the results, the proposed distribution performed better than the competing distributions.

scholarly journals SOME PROPERTIES OF BETA TRANSMUTED DAGUM DISTRIBUTION WITH APPLICATIONS

2020 ◽  
Vol 4 (2) ◽  
pp. 327-340
Author(s):  
Ahmed Ali Hurairah ◽  
Saeed A. Hassen
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Data Set ◽  
New Family ◽  
Method Of Maximum Likelihood ◽  
Dagum Distribution ◽  
New Distribution

In this paper, we introduce a new family of continuous distributions called the beta transmuted Dagum distribution which extends the beta and transmuted familys. The genesis of the beta distribution and transmuted map is used to develop the so-called beta transmuted Dagum (BTD) distribution. The hazard function, moments, moment generating function, quantiles and stress-strength of the beta transmuted Dagum distribution (BTD) are provided and discussed in detail. The method of maximum likelihood estimation is used for estimating the model parameters. A simulation study is carried out to show the performance of the maximum likelihood estimate of parameters of the new distribution. The usefulness of the new model is illustrated through an application to a real data set.

scholarly journals The Topp Leone Generalized Inverted Kumaraswamy Distribution: Properties and Applications

2019 ◽  
pp. 1-15 ◽  
Author(s):  
Hesham Reyad ◽  
Farrukh Jamal ◽  
Soha Othman ◽  
Nagla Yahia
Keyword(s):  
Stochastic Ordering ◽  
Quantile Function ◽  
Continuous Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Kumaraswamy Distribution ◽  
Mathematical Properties ◽  
Probability Weighted Moments ◽  
Method Of Maximum Likelihood ◽  
New Distribution

We propose a new four parameters continuous model called the Topp Leone generalized inverted Kumaraswamy distribution which extends the generalized inverted Kumaraswamy distribution. Basic mathematical properties of the new distribution are invstigated such as; quantile function, raw and incomplete moments, generating functions, probability weighted moments, order statistics, Rényi entropy, stochastic ordering and stress strength model. The method of maximum likelihood is used to estimate the model parameters of the new distribution. A Monte Carlo simulation is conducted to examine the behavior of the parameter estimates. The applicability of the new model is demonstrated by means of two real applications.

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