Ibrahim Elbatal’s scientific contributions

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Publications (4)


MLEs and SEs values for the relief times data.
C₁, C₂, C₃, C₄, í µí°´ µí°´ * , í µí° ¶ * , K.S. and (p-value) for the relief times data. Models C₁, C₂, C₃, C₄ í µí°´ µí°´ * , í µí° ¶ * K.S. (p-value)
MLEs and SEs values for the survival times data.
On Erlang-Truncated Exponential Distribution: Theory and Application
  • Article
  • Full-text available

March 2021

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41 Reads

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2 Citations

Pakistan Journal of Statistics and Operation Research

Ibrahim Elbatal

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A. Aldukeel

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

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The Odd Log-Logistic Poisson Inverse Rayleigh Distribution: Statistical Properties and Applications

December 2020

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20 Reads

Pakistan Journal of Statistics and Operation Research

In this work, a new extension of the Inverse Rayleigh model is proposed and studied. We derive some of its fundamental properties. We assess the performance of the maximum likelihood estimators via a simulation study. The importance of the new model is shown via two applications to real data sets. The new model is better fit than other important competitive models based on two real data sets.


The MLEs and the S.Es (in parentheses) of the model parameters for the first data set Model MLEs and SEsâˆˆˆˆ SEsˆSEsâ SEs∠SEsâˆ SEsâˆˆ SEsâˆˆ SEsâˆˆˆ SEsâˆˆˆ SEsâˆˆˆˆ SEsâˆˆˆˆ
The MLEs and the S.Es (in parentheses) of the parameters for the second data set Model MLEsâˆˆˆˆ MLEsˆMLEsâ MLEs∠MLEsâˆ MLEsâˆˆ MLEsâˆˆ MLEsâˆˆˆ MLEsâˆˆˆ MLEsâˆˆˆˆ MLEsâˆˆˆˆ
On the Exponentiated Weibull Rayleigh Distribution

August 2019

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578 Reads

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20 Citations

Gazi University Journal of Science

Highlights • We introduce a new four parameter distribution called exponentiated Weibull Rayligh distribution. • We study some statistical properties of the new model. • We use the maximum likelihood method to estimate the parameters of the distribution. • We make simulation results by using Mathematica 9. • The new model is very flexible and include some special models. Article Info Abstract A new four-parameter probability model, referred to the exponentiated Weibull Rayleigh (EWR) distribution, is introduced. Essential statistical properties of the distribution are considered. The maximum likelihood estimators of population parameters are given in case of complete sample. Simulation study is carried out to estimate the model parameters of EWR distribution. Additionally, parameter estimators are given in case of Type II censored samples. We come up with two applications to confirm the usefulness of the proposed distribution.


MLEs (standard errors in parentheses).
MODIFIED BETA GENERALIZED LINEAR FAILURE RATE DISTRIBUTION: THEORY AND APPLICATIONS

January 2019

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216 Reads

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3 Citations

Journal of Prime Research in Mathematics

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Ibrahim Elbatal

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[...]

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In this paper we introduce a new comprehensive six-parameter distribution called the modified beta generalized linear failure rate distribution. One of the interest of this distribution is to generalize some well-known flexible distributions discussed in the literature, such as (i) the beta linear failure rate distribution, (ii) the generalized linear failure rate distribution, (iii) the beta exponential distribution, (iv) the beta Rayleigh distribution and (v) the generalized exponential distribution, among others. We derive some of its statistical properties, including the moments, the moment generating function, the quantile function, the order statistics and the mean deviations. We propose the method of maximum likelihood for estimating the model parameters. A simulation study is performed in order to investigate the performance of the maximum likelihood estima-tors. A real data set is used to illustrate the importance and the flexibility of the new distribution.

Citations (3)


... Ali et al. (2020) [1] introduced a new discrete Time Between Events control chart following discrete Weibull distribution, by derived the design of the proposed chart analytically and discussed numerically. Elbatal and Aldukeel (2021) [2] discussed the McDonald Erlang-truncated exponential distribution with three shape parameters. Sayyed et al. (2021) [15] studied the effect of inspection error on cumulative sum (CUSUM) control charts for controlling the parameters of a random variable under Erlang-truncated exponential distribution, also derived expression for the parameter of the CUSUM chart. ...

Reference:

Discrete Erlang-truncated exponential distribution
On Erlang-Truncated Exponential Distribution: Theory and Application

Pakistan Journal of Statistics and Operation Research

... Many researchers constructed generalizations of the GLE distribution. For instance, various univariate extensions of the GLFR distribution have been introduced, including the generalized linear exponential (GLE) [2], beta linear failure rate [3], exponentiated GLFR [4], generalized exponential LFR [5], odd generalized exponential GLFR [6], inverted GLFR [7], Marshall-Olkin extended GLFR [8], truncated Cauchy power LFR [9] and modified beta GLFR [10] distributions. ...

MODIFIED BETA GENERALIZED LINEAR FAILURE RATE DISTRIBUTION: THEORY AND APPLICATIONS

Journal of Prime Research in Mathematics

... The radar model's reliability system was enhanced [11] using the two-parameter Weibull distribution as the basis. The Exponentiated Weibull Rayleigh Distribution was introduced and its properties were investigated [12]. The linear-exponential distribution function was assessed based on systems' reliability [13]. ...

On the Exponentiated Weibull Rayleigh Distribution

Gazi University Journal of Science