scholarly journals Odoma Distribution and Its Application

2019 ◽  
pp. 1-11
Author(s):  
C. C. Odom ◽  
M. A. Ijomah
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Survival Function ◽  
Real Life ◽  
Rate Function ◽  
Mean Residual Life ◽  
Mathematical Properties ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
New Distribution

In this study, a new continuous one parameter lifetime distribution is proposed. Its mathematical properties such as moments, order statistics, entropy, survival function, hazard rate function and mean residual life function are derived. The new distribution is applied to real-life data from engineering and the method of maximum likelihood is used to estimate the parameter. The goodness-of-fit of the new distribution shows its better fit to the data than some competing distributions.

scholarly journals A Two-parameter Rama Distribution

2019 ◽  
pp. 365-382
Author(s):  
U. Umeh Edith ◽  
T. Umeokeke Ebele ◽  
A. Ibenegbu Henrietta
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Real Life ◽  
Stochastic Ordering ◽  
Rate Function ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Estimation Of Parameters ◽  
Lorenz Curves ◽  
Two Parameter

In this paper, a two-parameter Rama distribution is proposed. This is coined from Lindley distribution and Rama distribution. Its mathematical and statistical properties which include its shapes, moment, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation; Bonferroni and Lorenz curves are also discussed. The estimation of parameters has been X-rayed using methods of moment and maximum likelihood. Also AIC and BIC are used to test for the goodness of fit of the model which is applied to a real life data of hepatitis B patients. This new distribution is compared with Rama, 2-parameter Akash, 2-parameter Lindley, Akash, Shanker, Ishita, Lindley and Exponential distributions in order to determine the efficiency of the new model.

scholarly journals On the inferences and applications of transmuted exponential Lomax distribution

2018 ◽  
Vol 6 (1) ◽  
pp. 30
Author(s):  
Umar Kabir ◽  
Terna Godfrey IEREN
Keyword(s):  
Real Life ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Probability Density Function Pdf ◽  
New Distribution ◽  
Better Than

This article proposed a new distribution referred to as the transmuted Exponential Lomax distribution as an extension of the popular Lomax distribution in the form of Exponential Lomax by using the Quadratic rank transmutation map proposed and studied in earlier research. Using the transmutation map, we defined the probability density function (PDF) and cumulative distribution function (CDF) of the transmuted Exponential Lomax distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Lomax distribution using three real-life data sets. The results obtained indicated that TELD performs better than the other distributions comprising power Lomax, Exponential-Lomax, and the Lomax 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 The beta Gumbel distribution

2004 ◽  
Vol 2004 (4) ◽  
pp. 323-332 ◽  
Author(s):  
Saralees Nadarajah ◽  
Samuel Kotz
Keyword(s):  
Hazard Rate ◽  
Gumbel Distribution ◽  
Random Variable ◽  
Rate Function ◽  
Comprehensive Treatment ◽  
Hazard Rate Function ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
New Distribution ◽  
Skewness And Kurtosis

The Gumbel distribution is perhaps the most widely applied statistical distribution for problems in engineering. In this paper, we introduce a generalization—referred to as the beta Gumbel distribution—generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of this new distribution. We derive the analytical shapes of the corresponding probability density function and the hazard rate function and provide graphical illustrations. We calculate expressions for thenth moment and the asymptotic distribution of the extreme order statistics. We investigate the variation of the skewness and kurtosis measures. We also discuss estimation by the method of maximum likelihood. We hope that this generalization will attract wider applicability in engineering.

scholarly journals On the Properties and Applications of Lomax-Exponential Distribution

2018 ◽  
pp. 1-13
Author(s):  
Terna Godfrey Ieren ◽  
David Adugh Kuhe
Keyword(s):  
Exponential Distribution ◽  
Survival Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Random Variable ◽  
Quantile Function ◽  
Life Data ◽  
Life Problems ◽  
Real Life Data ◽  
New Distribution

The Exponential distribution is memoryless and has a constant failure rate which makes it unsuitable for real life problems. This paper introduces a new distribution powered by an exponential random variable which gives a more flexible model for modelling real-life data. This new extension of the Exponential Distribution is called “Lomax-Exponential distribution (LED)”. The extension of the new distribution became possible with the help of a Lomax generator proposed by [1]. This paper derives and studies some expressions for various statistical properties of the new distribution including distribution function, moments, quantile function, survival function and hazard function known as reliability functions. The inference for the Lomax-Exponentially distributed random variable were investigated based on some plots of the distribution and others revealed its behaviour and usefulness in real life situations. The parameters of the distribution are estimated using the method of maximum likelihood estimation. The performance of the new Lomax-Exponential distribution has been tested and compared to the Weibull-Exponential, Transmuted Exponential and the conventional Exponential distribution using three real life data sets.  

scholarly journals Extended Rayleigh Distribution: Properties and Application to Failure Data

2021 ◽  
pp. 1-8
Author(s):  
Aladesuyi Alademomi ◽  
Philips Samuel Ademola ◽  
Adefolarin Adekunle David
Keyword(s):  
Real Life ◽  
Quantile Function ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Data Set ◽  
New Model ◽  
Failure Data ◽  
Mathematical Properties ◽  
Real Life Data ◽  
Method Of Maximum Likelihood

This paper introduces a new three parameter Rayleigh distribution which generalizes the Rayleigh distribution. The new model is referred to as Extended Rayleigh (ER) distribution. Various mathematical properties of the new model including ordinary and incomplete moment, quantile function, generating function are derived. We propose the method of maximum likelihood for estimating the model parameters. A real life data set is used to compare the flexibility of the new model with other models.

A Two-Parameter Pranav Distribution with Properties and Its Application.

2019 ◽  
Author(s):  
Edith Umeh ◽  
Amuche Ibenegbu
Keyword(s):  
Goodness Of Fit ◽  
Residual Life ◽  
Real Life ◽  
Lifetime Distribution ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Hypertensive Patients ◽  
Study Results ◽  
Two Parameter

Introduction: Lifetime distribution has drawn so much attention in recent research, and this has lead to the development of new lifetime distribution. Addition of parameters to the existing distribution makes the distribution more flexible and reliable and applicable model has become the focus of the recent search. This paper proposed a two-parameter Pranav distribution which has its base from a one-parameter Pranav and Ishita distribution. Methods Two parameter Pranav distribution was proposed. Mathematical and statistical properties of the distribution which includes; moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation, Bonferroni and Lorenz curves were developed. Other lifetime distributions such as Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions were considered in the study. Results: This new distribution was compared with two-parameter Akash, Lindley, one parameter Pranav, Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions to determine the efficiency of the new model. The estimation of parameters has been X-rayed using the method of moments and maximum likelihood. Also, AIC and BIC were used to test for the goodness of fit of the model which was applied to a real-life data of hypertensive patients. The results show that the new two-parameter Pranav distribution has the lowest value of AIC and BIC Conclusion: Based on the AIC and BIC values we can conclude that the two-parameter Pranav is more efficient than the other distribution for modeling survival of hypertensive patients. Hence two-parameter Pranav can be seen as an important distribution in modeling lifetime data.

scholarly journals A Study of Some Properties and Goodness-of-Fit of a Gompertz-Rayleigh Model

2020 ◽  
pp. 18-31
Author(s):  
Fadimatu Bawuro Mohammed ◽  
Kabiru Ahmed Manju ◽  
Umar Kabir Abdullahi ◽  
Makama Musa Sani ◽  
Samson Kuje
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Likelihood Estimation ◽  
Rayleigh Distribution ◽  
Parameter Distribution ◽  
Applied Statistics ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Wide Range

The Rayleigh was obtained from the amplitude of sound resulting from many important sources by Rayleigh. It is continuous probability distribution with a wide range of applications such as in life testing experiments, reliability analysis, applied statistics and clinical studies. However, it is not flexible enough for modeling heavily skewed datasets as compared to compound distributions. In this paper, we introduce a new extension of the Rayleigh distribution by using a Gompertz-G family of distributions. This paper defines and studies a three-parameter distribution called “Gompertz-Rayleigh distribution”. Some properties of the proposed distribution are derived and discussed comprehensively in this paper and the three parameters are estimated using the method of maximum likelihood estimation. The goodness-of-fit of the proposed distribution is also evaluated by fitting it in comparison with some other existing distributions using a real life data.

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 Samade Probability Distribution: Its Properties and Application to Real Lifetime Data

2021 ◽  
pp. 1-11
Author(s):  
Samuel Aderoju
Keyword(s):  
Survival Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Reliability Function ◽  
Entropy Measure ◽  
Lifetime Distributions ◽  
Mathematical Properties ◽  
Real Life Data ◽  
Proposed Model ◽  
First Four Moments

A new two-parameter lifetime distribution has been proposed in this study. The distribution is called Samade distribution. The model is motivated by the wide use of the lifetime models derived from the mixture of gamma and exponential distributions. Its mathematical properties which include the first four moments, variance as well as coefficient of variation, reliability function, hazard function, survival function, Renyi entropy measure and distribution of order statistics have been successfully derived. The maximum likelihood estimation of its parameters and application to real life data have been discussed. Application of this model to three real datasets shown that the proposed model yields a satisfactorily better fit than other existing lifetime distributions. The comparism of goodness-of-fits were established using -2Loglikelihood, AIC and BIC. 

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