scholarly journals On modified Burr III-power distribution: Development, properties, characterizations, and applications

2019 ◽  
Vol 52 (2) ◽  
pp. 151-171
Author(s):  
FIAZ AHMAD BHATTI
Keyword(s):  
Maximum Likelihood ◽  
Power Distribution ◽  
Residual Life ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Inequality Measures ◽  
Failure Times ◽  
Reversal Time ◽  
Potential Use

In this paper, a flexible distribution with increasing, bathtub and inverted bathtub hazard rate called Modified Burr III-Power (MBIII-Power) is developed on the basis of the generalized Pearson differential equation. The density function of MBIII-Power is arc, exponential and positively skewed shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBIII-Power distribution is characterized via different techniques. Parameters of MBIII-Power distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). Potential use of MBIII-Power distribution is demonstrated by its application to two data sets: serum-reversal time (in days) of children born from HIV-infected mothers and failure times of device data.

scholarly journals On The Modified Burr XII-Power Distribution: Development, Properties, Characterizations and Applications

2019 ◽  
pp. 61-85
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Mustafa Ç. Korkmaz ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Power Distribution ◽  
Residual Life ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Survival Times ◽  
Quarterly Earnings ◽  
Inequality Measures

In this paper, a flexible lifetime distribution with increasing, decreasing and bathtub hazard rate called the Modified Burr XII-Power (MBXII-Power) is developed on the basis of the T-X family technique. The density function of the MBXII-Power is arc, exponential, left-skewed, right-skewed, J, reverse-J and symmetrical shaped.  Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBXII-Power distribution is characterized via different techniques. Parameters of the MBXII-Power distribution are estimated using maximum likelihood method. The simulation study is performed on the basis of graphical results to see the performance of maximum likelihood estimates (MLEs) of the MBXII-Power distribution. The potentiality of the MBXII-Power distribution is demonstrated by its application to real data sets: survival times of pigs, survival times of patients and quarterly earnings

scholarly journals Cubic Rank Transmuted Modified Burr III Pareto Distribution: Development, Properties, Characterizations and Applications

2018 ◽  
Vol 8 (1) ◽  
pp. 94
Author(s):  
Fiaz Ahmad Bhatti ◽  
G.G. Hamedani ◽  
Wenhui Sheng ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Residual Life ◽  
Glass Fibers ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Inequality Measures ◽  
P Distribution

In this paper, a flexible lifetime distribution called Cubic rank transmuted modified Burr III-Pareto (CRTMBIII-P) is developed on the basis of the cubic ranking transmutation map. The density function of CRTMBIII-P is arc, exponential, left-skewed, right-skewed and symmetrical shaped. Descriptive measures such as moments, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The CRTMBIII-P distribution is characterized via ratio of truncated moments. Parameters of the CRTMBIII-P distribution are estimated using maximum likelihood method. The simulation study for the performance of the maximum likelihood estimates (MLEs) of the parameters of the CRTMBIII-P distribution is carried out. The potentiality of CRTMBIII-P distribution is demonstrated via its application to the real data sets: tensile strength of carbon fibers and strengths of glass fibers. Goodness of fit of this distribution through different methods is studied.

scholarly journals On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

scholarly journals A New Scale-Invariant Lindley Extension Distribution and Its Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Mohamed Kayid ◽  
Rayof Alskhabrah ◽  
Arwa M. Alshangiti
Keyword(s):  
Maximum Likelihood ◽  
Failure Rate ◽  
Residual Life ◽  
Rate Function ◽  
Likelihood Method ◽  
Mean Residual Life ◽  
Data Sets ◽  
Scale Invariant ◽  
Failure Rate Function ◽  
Right Censored Data

A new scale-invariant extension of the Lindley distribution and its power generalization has been introduced. The moments and the moment-generating functions of the proposed models have closed forms. The failure rate, the mean residual life, and the α -quantile residual life functions have been explored. The failure rate function of these models accommodates increasing, bathtub-shaped, and increasing then bathtub-shaped forms. The parameters of the models have been estimated by the maximum likelihood method for the complete and right-censored data. In a simulation study, the efficiency and consistency of the maximum likelihood estimator have been investigated. Then, the proposed models were fitted to four data sets to show their flexibility and applicability.

scholarly journals Inverse Lomax-Exponentiated G (IL-EG) Family of Distributions: Properties and Applications

2020 ◽  
pp. 48-64
Author(s):  
Jamilu Yunusa Falgore ◽  
Sani Ibrahim Doguwa
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Baseline Model ◽  
New Family ◽  
Family Of Distributions ◽  
Better Than

A new generator of continuous distributions called the Inverse Lomax-Exponentiated G family, which has three extra positive parameters is proposed. The structural properties of the new family that holds for any continuous baseline model including explicit density function expressions, moments, inequality measurements, moment generating function, reliability functions, Renyi and Shanon entropies, and distribution of order statistics are derived. A Monte Carlo simulation to test the efficiency of the maximum likelihood estimates is conducted. The application of the new sub-model to the two data sets using the maximum likelihood method indicates that the new model is better than the existing competitors.

scholarly journals A Novel Generalized Family of Distributions for Engineering and Life Sciences Data Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Najma Salahuddin ◽  
Alamgir Khalil ◽  
Wali Khan Mashwani ◽  
Habib Shah ◽  
Pijitra Jomsri ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Mean Squared Error ◽  
Residual Life ◽  
Parametric Estimation ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Mean Residual Life ◽  
Estimation Of Parameters ◽  
Lifetime Distributions ◽  
The Family

In this paper, a new method is proposed to expand the family of lifetime distributions. The suggested method is named as Khalil new generalized family (KNGF) of distributions. A special submodel, termed as Khalil new generalized Pareto (KNGP) distribution, is investigated from the family with one shape and two scale parameters. A number of mathematical properties of the submodel have been derived including moments, moment-generating function, quantile function, entropy measures, order statistics, mean residual life function, and maximum likelihood method for the estimation of parameters. The proposed distribution is very flexible in its nature covering several hazard rate shapes (symmetric and asymmetric). To examine the performance of the maximum likelihood estimates in terms of their bias and mean squared error using simulated samples, a simulation study is carried out. Furthermore, parametric estimation of the model is conferred using the method of maximum likelihood, and the practicality of the proposed family is illustrated with the help of real datasets. Finally, we hope that the new suggested flexible KNGF may produce useful models for fitting monotonic and nonmonotonic data related to survival analysis and reliability analysis.

scholarly journals New Regression Models Based on the Unit-Sinh-Normal Distribution: Properties, Inference, and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1231
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón
Keyword(s):  
Maximum Likelihood ◽  
Regression Models ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Random Variable ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Modeling Data ◽  
Positive Support

In this paper, two new distributions were introduced to model unimodal and/or bimodal data. The first distribution, which was obtained by applying a simple transformation to a unit-Birnbaum–Saunders random variable, is useful for modeling data with positive support, while the second is appropriate for fitting data on the (0,1) interval. Extensions to regression models were also studied in this work, and statistical inference was performed from a classical perspective by using the maximum likelihood method. A small simulation study is presented to evaluate the benefits of the maximum likelihood estimates of the parameters. Finally, two applications to real data sets are reported to illustrate the developed methodology.

scholarly journals A New Lifetime Model: Copulas, Properties and Real Lifetime Data Applications

2021 ◽  
pp. 195-211
Author(s):  
Wahid Shehata
Keyword(s):  
Maximum Likelihood ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Finite Sample ◽  
Failure Rate Function ◽  
Failure Times ◽  
Lifetime Model ◽  
New Distribution

A new four parameter lifetime model called the Weibullgeneralized Lomax is proposed and studied.  The new density function can be "right skewed", "symmetric" and "left skewed" and its corresponding failure rate function can be "monotonically decreasing", " monotonically increasing" and "constant". The skewness of the new distribution can negative and positive. The maximum likelihood method is employed and used for estimating the model parameters. Using the "biases" and "mean squared errors", we performed simulation experiments for assessing the finite sample behavior of the maximum likelihood estimators. The new model deserved to be chosen as the best model among many well-known Lomax extension such as exponentiated Lomax, gamma Lomax, Kumaraswamy Lomax, odd log-logistic Lomax, Macdonald Lomax, beta Lomax, reduced odd log-logistic Lomax, reduced Burr-Hatke Lomax, reduced WG-Lx, special generalized mixture Lomax and the standard Lomax distributions in modeling the "failure times" and the "service times" data sets.

scholarly journals The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 650 ◽  
Author(s):  
Abdullah M. Almarashi ◽  
Mohammed Elgarhy ◽  
Farrukh Jamal ◽  
Christophe Chesneau
Keyword(s):  
Maximum Likelihood ◽  
Numerical Study ◽  
Stochastic Ordering ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Wide Sense ◽  
Rate Functions ◽  
Generated Family ◽  
Family Of Distributions

In this paper, we propose a generalization of the so-called truncated inverse Weibull-generated family of distributions by the use of the power transform, adding a new shape parameter. We motivate this generalization by presenting theoretical and practical gains, both consequences of new flexible symmetric/asymmetric properties in a wide sense. Our main mathematical results are about stochastic ordering, uni/multimodality analysis, series expansions of crucial probability functions, probability weighted moments, raw and central moments, order statistics, and the maximum likelihood method. The special member of the family defined with the inverse Weibull distribution as baseline is highlighted. It constitutes a new four-parameter lifetime distribution which brightensby the multitude of different shapes of the corresponding probability density and hazard rate functions. Then, we use it for modelling purposes. In particular, a complete numerical study is performed, showing the efficiency of the corresponding maximum likelihood estimates by simulation work, and fitting three practical data sets, with fair comparison to six notable models of the literature.

scholarly journals The Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1114
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón ◽  
María Martínez-Guerra
Keyword(s):  
Power Distribution ◽  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Score Functions ◽  
New Family ◽  
Two Parameters ◽  
Family Of Distributions

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

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