Weibull-Normal Distribution and its Applications

Famoye, Felix; Akarawak, Eno E. E.; Ekum, Matthew Iwada

doi:10.2991/jsta.2018.17.4.12

Cited by 13 publications

(11 citation statements)

References 9 publications

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“…By using the Weibull-G framework given in (5), we derived the CDF of Weibull Inverse Rayleigh (WIR) distribution by putting (7) in (5) to have…”

Section: The New Three-parameters Weibull-inverse Rayleigh (Wir) Distributionmentioning

confidence: 99%

“…Weibull-Gamma {Log-logistic} [5]; Weibull-Exponential{Log-logistic}, Gamma-Exponential{Log-logistic} and Normal-Exponential { Log-logistic } [ 6 ]; Weibull-Normal { Log-logistic } [7]; and [8]which exploited the statistical properties of Odd Lomax-Exponential{Log-logistic} distribution. All distributions are members of the T-R{log-logistic} family that have a probability density function with three components vis-a-vis the hazard function, survival function, and the odd-ratio.…”

Section: Introductionmentioning

confidence: 99%

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A New Three-Parameter Weibull Inverse Rayleigh Distribution: Theoretical Development and Applications

Ogunsanya¹,

Yahya²,

Adegoke³

et al. 2021

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In this work, a three-parameter Weibull Inverse Rayleigh (WIR) distribution is proposed. The new WIR distribution is an extension of a one-parameter Inverse Rayleigh distribution that incorporated a transformation of the Weibull distribution and Log-logistic as quantile function. The statistical properties such as quantile function, order statistic, monotone likelihood ratio property, hazard, reverse hazard functions, moments, skewness, kurtosis, and linear representation of the new proposed distribution were studied theoretically. The maximum likelihood estimators cannot be derived in an explicit form. So we employed the iterative procedure called Newton Raphson method to obtain the maximum likelihood estimators. The Bayes estimators for the scale and shape parameters for the WIR distribution under squared error, Linex, and Entropy loss functions are provided. The Bayes estimators cannot be obtained explicitly. Hence we adopted a numerical approximation method known as Lindley's approximation in other to obtain the Bayes estimators. Simulation procedures were adopted to see the effectiveness of different estimators. The applications of the new WIR distribution were demonstrated on three real-life data sets. Further results showed that the new WIR distribution performed credibly well when compared with five of the related existing skewed distributions. It was observed that the Bayesian estimates derived performs better than the classical method.

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“…By using the Weibull-G framework given in (5), we derived the CDF of Weibull Inverse Rayleigh (WIR) distribution by putting (7) in (5) to have…”

Section: The New Three-parameters Weibull-inverse Rayleigh (Wir) Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Three-Parameter Weibull Inverse Rayleigh Distribution: Theoretical Development and Applications

Ogunsanya¹,

Yahya²,

Adegoke³

et al. 2021

View full text Add to dashboard Cite

show abstract

“…In the literature, many authors have used this T-R{Y} framework to develop probability distributions, such as Aljarrah et al [16]; Alzatraah et al [19,20]; Nasir et al [25,26]; Jamal et al [27,28]; Zubair et al [21]; Famoye et al [22]; and Jamal and Nasir [29]. None of these authors has generalized Dagum distribution using this framework.…”

Section: Proposed T-dagum{y} Classmentioning

confidence: 99%

“…Hazard Function of EEDL Distribution. Let X be a random variable that follows an EEDL distribution, with pdf and survival function given in (22) and (27), respectively; then, its hazard function is given by…”

Section: Lemma 3 E Quantile Function Of the Eedl Distribution For P mentioning

confidence: 99%

“…One major importance of providing new distribution through the quantile function of an existing distribution is that the newly formed distribution has the tendency of having higher flexibility in handling bimodality in datasets and it is a weighted hazard function of the baseline distribution (Dagum distribution in this case). For more detailed informations on the importance of using this method, T-R {Y}, see Aljarrah et al [16]; Alzaatreh et al [19,20]; Zubair et al [21]; and Famoye et al [22]. Also, for detailed knowledge of Dagum distribution, see Bandourian et al [4]; Kleiber and Kotz [2]; Kleiber [3]; Domma and Condino [5]; Oluyede and Rajasooriya [6]; Oluyede and Ye [7]; Oluyede et al [8]; Huang and Oluyede [9]; Silva et al [10]; Shahzad and Asghar [11]; Oluyede et al [12]; Nasiru et al [13]; and Bakouch et al [14].…”

Section: Introductionmentioning

confidence: 99%

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T-Dagum: A Way of Generalizing Dagum Distribution Using Lomax Quantile Function

Ekum

Adamu

Akarawak

2020

Journal of Probability and Statistics

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Recently, different distributions have been generalized using the T-R {Y} framework but the possibility of using Dagum distribution has not been assessed. The T-R {Y} combines three distributions, with one as a baseline distribution, with the strength of each distribution combined to produce greater effect on the new generated distribution. The new generated distributions would have more parameters but would have high flexibility in handling bimodality in datasets and it is a weighted hazard function of the baseline distribution. This paper therefore generalized the Dagum distribution using the quantile function of Lomax distribution. A member of T-Dagum class of distribution called exponentiated-exponential-Dagum {Lomax} (EEDL) distribution was proposed. The distribution will be useful in survival analysis and reliability studies. Different characterizations of the distribution are derived, such as the asymptotes, stochastic ordering, stress-strength analysis, moment, Shannon entropy, and quantile function. Simulated and real data are used and compared favourably with existing distributions in the literature.

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Normal-Power-Logistic Distribution: Properties and Application in Generalized Linear Model

Ekum

Adamu

Akarawak

2022

J Indian Soc Probab Stat

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The applications of Normal distribution in literature are verse, the new modified univariate normal power distribution is a new distribution which is adequate for modelling bimodal data. There are many data that would have been modelled by normal distribution, but because of their bimodality, they are not, since normal distribution is unimodal. In this paper, a new extension of the normal linear model called the normal-Power generalized linear model, derived from the T-Power Logistic framework is presented. The statistical properties of the distribution and the proposed model were derived such as quantiles, median, mode, robust skewness, robust kurtosis and moment. The maximum likelihood estimation method was considered to obtain the unknown model parameters. Three real data sets were analyzed to demonstrate the flexibility and usefulness of the proposed model. The new model would be very useful as alternative in cases where skewed or bimodal response variables, which are not well fitted with normal linear model.

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Weibull-Normal Distribution and its Applications

Cited by 13 publications

References 9 publications

A New Three-Parameter Weibull Inverse Rayleigh Distribution: Theoretical Development and Applications

A New Three-Parameter Weibull Inverse Rayleigh Distribution: Theoretical Development and Applications

T-Dagum: A Way of Generalizing Dagum Distribution Using Lomax Quantile Function

Normal-Power-Logistic Distribution: Properties and Application in Generalized Linear Model

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