scholarly journals Odd Lindley-Rayleigh Distribution: Its Properties and Applications to Simulated and Real Life Datasets

2020 ◽  
pp. 63-88
Author(s):  
Terna Godfrey Ieren ◽  
Sauta Saidu Abdulkadir ◽  
Adekunle Abdulmumeen Issa
Keyword(s):  
Real Life ◽  
Rayleigh Distribution ◽  
Information Criteria ◽  
The Other ◽  
Cumulative Distribution ◽  
Parameter Estimates ◽  
Probability Models ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Two Parameters

This article develops an extension of the Rayleigh distribution with two parameters and greater flexibility which is an improvement over Lindley distribution, Rayleigh distribution and other generalizations of the Rayleigh distribution. The new model is known as “odd Lindley-Rayleigh Distribution”. The definitions of its probability density function and cumulative distribution function using the odd Lindley-G family of distributions are provided. Some properties of the new distribution are also derived and studied in this article with applications and discussions. The estimation of the unknown parameters of the proposed distribution is also carried out using the method of maximum likelihood. The performance of the proposed probability distribution is compared to some other generalizations of the Rayleigh distribution using three simulated datasets and a real life dataset. The results obtained are compared using the values of some information criteria evaluated with the parameter estimates of the fitted distributions based on the four datasets and it is revealed that the proposed distribution outperforms all the other fitted distributions. This performance has shown that the odd Lindley-G family of distribution is an adequate generator of probability models and that the odd Linley-Rayleigh distribution is a very flexible distribution for fitting different kinds of datasets better than the other generalizations of the Rayleigh distribution considered in this study.

scholarly journals The Maxwell – Exponential Distribution: Theory and Application to Lifetime Data

2021 ◽  
Vol 3 (2) ◽  
pp. 65-80
Author(s):  
Usman Aliyu Abdullahi ◽  
Ahmad Abubakar Suleiman ◽  
Aliyu Ismail Ishaq ◽  
Abubakar Usman ◽  
Aminu Suleiman
Keyword(s):  
Exponential Distribution ◽  
Survival Function ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Information Criteria ◽  
Cumulative Distribution ◽  
Two Parameters ◽  
Maximum Likelihood Estimation Method

Two parameters Maxwell – Exponential distribution was proposed using the Maxwell generalized family of distribution. The probability density function, cumulative distribution function, survival function, hazard function, quantile function, and statistical properties of the proposed distribution are discussed. The parameters of the proposed distribution have been estimated using the maximum likelihood estimation method. The potentiality of the estimators was shown using a simulation study. The overall assessment of the performance of Maxwell - Exponential distribution was determined by using two real-life datasets. Our findings reveal that the Maxwell – Exponential distribution is more flexible compared to other competing distributions as it has the least value of information criteria.

ON THE PROPERTIES AND APPLICATIONS OF A NEW EXTENSION OF EXPONENTIATED RAYLEIGH DISTRIBUTION

2021 ◽  
Vol 5 (2) ◽  
pp. 377-398
Author(s):  
Hussein Abdulsalam ◽  
Yahaya Abubakar ◽  
Hussaini Garba Dikko
Keyword(s):  
Hazard Function ◽  
Random Number Generator ◽  
Real Life ◽  
Reliability Function ◽  
Rayleigh Distribution ◽  
Estimation Methods ◽  
Experimental Investigations ◽  
Parameter Estimates ◽  
Unknown Parameters ◽  
Integrated Hazard

Statistical distributions already in existence are not the most appropriate model that adequately describes real-life data such as those obtained from experimental investigations. Therefore, there are needs to come up with their extended forms to give substitutive adaptable models. By adopting the method of Transformed-Transformer family of distributions, an extension of Exponentiated Rayleigh distribution titled Gompertz- Exponentiated Rayleigh (GOM-ER) distribution was proposed and proved to be valid. Some properties of the new distribution including random number generator, quartiles, distribution of smallest and largest order statistics, reliability function, hazard rate function, cumulative or integrated hazard function, odds function, non-central moments, moment generating function, mean, variance and entropy measures were derived.  Using the methods of maximum likelihood and maximum product of spacing, the four unknown parameters were estimated.  Shapes of the hazard function depicts that GOM-ER is a distribution that is strictly increasing while those of the PDF depicts that GOM-ER can be skewed or symmetrical. Two datasets were fitted to determine the flexibility of GOM-ER. Simulation study evaluates the consistency, accuracy and unbiasedness of the GOM-ER parameter estimates obtained from the two frequentist estimation methods adopted.

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 On the Properties and Applications of a Transmuted Lindley-Exponential Distribution

2019 ◽  
pp. 1-13
Author(s):  
Adamu Abubakar Umar ◽  
Innocent Boyle Eraikhuemen ◽  
Peter Oluwaseun Koleoso ◽  
Jerry Joel ◽  
Terna Godfrey Ieren
Keyword(s):  
Exponential Distribution ◽  
Continuous Distribution ◽  
Real Life ◽  
Likelihood Estimation ◽  
Good Evidence ◽  
Survival Times ◽  
Probability Models ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Better Than

The Quadratic rank transmutation map proposed for introducing skewness and flexibility into probability models with a single parameter known as the transmuted parameter has been used by several authors and is proven to be useful. This article uses this method to add flexibility to the Lindley-Exponential distribution which results to a new continuous distribution called “transmuted Lindley-Exponential distribution”. This paper presents the definition, validation, properties, application and estimation of unknown parameters of the transmuted Lindley-Exponential distribution using the method of maximum likelihood estimation. The new distribution has been applied to a real life dataset on the survival times (in days) of 72 guinea pigs and the result gives good evidence that the transmuted Lindley-Exponential distribution is better than the Lindley-Exponential distribution, Exponential distribution and Lindley distribution based on the dataset used.

scholarly journals An Exponentiated Odd Lindley Inverse Exponential Distribution and its Application to Infant Mortality and HIV Transmission Rates in Nigeria

2021 ◽  
pp. 12-30
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Gerald Ikechukwu Onwuka ◽  
Bassa Shiwaye Yakura ◽  
Hassan Allahde
Keyword(s):  
Infant Mortality ◽  
Exponential Distribution ◽  
Hiv Transmission ◽  
Transmission Rate ◽  
Probability Distributions ◽  
Real Life ◽  
Information Criteria ◽  
Infant Mortality Rate ◽  
Unknown Parameters ◽  
Inverse Exponential Distribution

Recently, researchers have shown much interest in developing new continuous probability distributions by adding one or two parameter(s) to the some existing baseline distributions. This act has been beneficial to the field of statistical theory especially in modeling of real life situations. Also, the exponentiated family as used in developing new distributions is an efficient method proposed and studied for defining more flexible continuous probability distributions for modeling real life data. In this study, the method of exponentiation has been used to develop a new distribution called “Exponentiated odd Lindley inverse exponential distribution”. Some properties of the proposed distribution and estimation of its unknown parameters has been done using the method of maximum likelihood estimation and its application to real life datasets. The new model has been applied to infant mortality rate and mother-to-child HIV transmission rate. The results of these two applications reveal that the proposed model is a better model compared to the other fitted existing models by some selection information criteria.

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 Statistical Inference of Left Truncated and Right Censored Data from Marshall–Olkin Bivariate Rayleigh Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2703
Author(s):  
Ke Wu ◽  
Liang Wang ◽  
Li Yan ◽  
Yuhlong Lio
Keyword(s):  
Statistical Inference ◽  
Information Matrix ◽  
Real Life ◽  
High Posterior Density ◽  
Rayleigh Distribution ◽  
Maximum Likelihood Estimates ◽  
Approximate Theory ◽  
Posterior Density ◽  
Unknown Parameters ◽  
Right Censored Data

In this paper, statistical inference and prediction issue of left truncated and right censored dependent competing risk data are studied. When the latent lifetime is distributed by Marshall–Olkin bivariate Rayleigh distribution, the maximum likelihood estimates of unknown parameters are established, and corresponding approximate confidence intervals are also constructed by using a Fisher information matrix and asymptotic approximate theory. Furthermore, Bayesian estimates and associated high posterior density credible intervals of unknown parameters are provided based on general flexible priors. In addition, when there is an order restriction between unknown parameters, the point and interval estimates based on classical and Bayesian frameworks are discussed too. Besides, the prediction issue of a censored sample is addressed based on both likelihood and Bayesian methods. Finally, extensive simulation studies are conducted to investigate the performance of the proposed methods, and two real-life examples are presented for illustration purposes.

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 A Continuous Poisson-Rayleigh Distribution: Its Properties and Applications

2021 ◽  
pp. 69-84
Author(s):  
Abraham Iorkaa Asongo ◽  
Innocent Boyle Eraikhuemen ◽  
Emmanuel Remi Omoboriowo ◽  
Isa Abubakar Ibrahim
Keyword(s):  
Maximum Likelihood ◽  
Probability Distribution ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Model Parameters ◽  
Method Of Maximum Likelihood ◽  
New Distribution

This article proposed a Poisson based continuous probability distribution called Poisson-Rayleigh distribution. Some properties of the new distribution such as quantile and reliability functions and other useful measures were obtained. The model parameters were estimated using the method of maximum likelihood. The usefulness of the new distribution was proven empirically using real life datasets.

scholarly journals On the Properties and Applications of Transmuted Odd Generalized Exponential-Exponential Distribution

2018 ◽  
pp. 1-14
Author(s):  
Jamila Abdullahi ◽  
Umar Kabir Abdullahi ◽  
Terna Godfrey Ieren ◽  
David Adugh Kuhe ◽  
Adamu Abubakar Umar
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Exponential Distribution ◽  
Cumulative Distribution Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Method Of Maximum Likelihood ◽  
Probability Density Function Pdf ◽  
New Distribution

This article proposed a new distribution referred to as the transmuted odd generalized exponential-exponential distribution (TOGEED) as an extension of the popular odd generalized exponential- exponential distribution by using the Quadratic rank transmutation map (QRTM) proposed and studied by [1]. Using the transmutation map, we defined the probability density function (pdf) and cumulative distribution function (cdf) of the transmuted odd generalized Exponential- Exponential 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 Exponential distribution using a real life dataset.  

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