A Gull Alpha Power Weibull distribution with applications to real and simulated data

Ijaz, Muhammad; Asim, Syed Muhammad; Alamgir,; Farooq, Muhammad; Khan, Sajjad Ahmad; Manzoor, Sadaf

doi:10.1371/journal.pone.0233080

Cited by 30 publications

(28 citation statements)

References 31 publications

(39 reference statements)

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“…Ali et.al [15] defined Alpha-Power Exponentiated Inverse Rayleigh distribution and its applications to real and simulated data. More recently Ijaz et.al [16][17][18] introduced a new scheme and families for generating the new probability distributions.…”

Section: Introductionmentioning

confidence: 99%

The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data

Badr

Ijaz

2021

PLoS ONE

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The paper addresses a new four-parameter probability distribution called the Exponentiated Exponential Burr XII or abbreviated as EE-BXII. We derive various statistical properties in addition to the parameter estimation, moments, and asymptotic confidence bounds. We estimate the precision of the maximum likelihood estimators via a simulation study. Furthermore, the utility of the proposed distribution is evaluated by using two lifetime data sets and the results are compared with other existing probability distributions. The results clarify that the proposed distribution provides a better fit to these data sets as compared to the existing probability distributions.

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Section: Introductionmentioning

confidence: 99%

The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data

Badr

Ijaz

2021

PLoS ONE

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“…For example, Ijaz et.al. [1] produced a new family of lifetime distributions and discussed its various statistical properties. e probability function of [1] can increase the reliability than others for the lifetime data analysis.…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

A Novel Approach to Increase the Goodness of Fits with an Application to Real and Simulated Data Sets

Farooq

Zaman

Ijaz

et al. 2021

Mathematical Problems in Engineering

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In practice, the data sets with extreme values are possible in many fields such as engineering, lifetime analysis, business, and economics. A lot of probability distributions are derived and presented to increase the model flexibility in the presence of such values. The current study also focuses on investigations to derive a new probability model New Flexible Family (NFF) of distributions. The significance of NFF is carried out using the Weibull distribution called New Flexible Weibull distribution or in short NFW. Various mathematical properties of NFW have been discussed including the estimation of parameters and entropy measures. Two real data sets with extreme values and a simulation study have been conducted so as to delineate the importance of NFW. Furthermore, NFW is compared with other existing probability distributions; numerically, it has been observed that the new mechanism of producing the lifetime probability distributions plays a significant role in making predictions about the population than others using the data sets with extreme values.

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“…Þ; Elbatal et al 13 proposed a new Alpha power transformed family of distributions G x ð Þα G x ð Þ =α Â Ã ; and recently, Ijaz et al 14 proposed a Gull alpha power Weibull family αG x ð Þ=α G x ð Þ Â Ã ; among others.…”

Section: Introductionmentioning

confidence: 99%

A new modified Lehmann type – II G class of distributions: exponential distribution with theory, simulation, and applications to engineering sector

et al. 2021

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Background: Modeling against non-normal data a challenge for theoretical and applied scientists to choose a lifetime model and expect to perform optimally against experimental, reliability engineering, hydrology, ecology, and agriculture sciences, phenomena. Method: We have introduced a new G class that generates relatively more flexible models to its baseline and we refer to it as the new modified Lehmann Type – II (ML–II) G class of distributions. A list of new members of ML–II-G class is developed and as a sub-model the exponential distribution, known as the ML-II-Exp distribution is considered for further discussion. Several mathematical and reliability characters along with explicit expressions for moments, quantile function, and order statistics are derived and discussed in detail. Furthermore, plots of density and hazard rate functions are sketched out over the certain choices of the parametric values. For the estimation of the model parameters, we utilized the method of maximum likelihood estimation. Results: The applicability of the ML–II–G class is evaluated via ML–II–Exp distribution. ML–II–Exp distribution is modeled to four suitable lifetime datasets and the results are compared with the well-known competing models. Some well recognized goodness–of–fit including -Log-likelihood (-LL), Anderson-Darling (A*), Cramer-Von Mises (W*), and Kolmogorov-Smirnov (K-S) test statistics are considered for the selection of a better fit model. Conclusion: The minimum value of the goodness–of–fit is the criteria of a better fit model that the ML–II–Exp distribution perfectly satisfies. Hence, we affirm that the ML–II–Exp distribution is a better fit model than its competitors.

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A Gull Alpha Power Weibull distribution with applications to real and simulated data

Cited by 30 publications

References 31 publications

The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data

The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data

A Novel Approach to Increase the Goodness of Fits with an Application to Real and Simulated Data Sets

A new modified Lehmann type – II G class of distributions: exponential distribution with theory, simulation, and applications to engineering sector

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