Unit Nadarajah and Haghighi Distribution: Properties and Applications in Quality Control

Shah, Ismail; Iqbal, Brikhna; Akram, Muhammad Farhan; Ali, Sajid; Dey, Sanku

doi:10.24200/sci.2021.57302.5167

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…X = e −Y Unit Weibull [12] Unit Gompertz [13] Unit Rayleigh [14] Unit gamma/Gompertz [15] Unit Gamma [16] The log-xgamma [17] Unit generalized half-normal [18] Unit Chen [19] Unit Nadarajah and Haghighi [20] Unit Inverse Guassian [21] Unit Burr-XII [22] Unit Power Logarithmic [23] X = Y ∕1 + Y One parameter unit Lindley [24] Modified unit Burr-III [25] X = 1∕1 + Y One parameter new unit Lindley [26] Y = 1 − (1 + X) − 1…”

Section: Transformation Referenced Unit-bounded Interval Distributionsmentioning

confidence: 99%

Study of a bounded interval perks distribution with quantile regression analysis

Al‐Essa,

Shafiq,

Ozonur

et al. 2024

Statistical Analysis

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In this article, a novel bounded interval model called the unit‐Perks model is developed by suitably transforming the positive random variable of the Perks distribution. Numerous statistical features of the bounded interval Perks model are being explored based on the expansion of the density function. Eight distinct estimation approaches are being used to estimate the parameters of the unit‐Perks model. A throughout simulation analysis is also included to evaluate the precision of the resulting estimators from eight estimating approaches. Two real bounded interval data sets are being utilized to investigate the practical applicability of the unit‐Perks model. A comparison is also made to determine which method of estimation works better for the given model. According to a comparison of eight different estimation approaches, the maximum likelihood estimation approach outperformed than the other seven estimating approaches. The unit‐perks model is then used to introduce the quantile regression model named as quantile unit‐Perks distribution. Application to real data set for the quantile unit‐Perks distribution is also performed. The quantile residuals are used for the residual analysis of the fitted regression model. On the basis of mathematical, computational, and pictorial evidences, it is concluded that the presented model exhibited greater modeling capabilities.

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Section: Transformation Referenced Unit-bounded Interval Distributionsmentioning

confidence: 99%

Study of a bounded interval perks distribution with quantile regression analysis

Al‐Essa,

Shafiq,

Ozonur

et al. 2024

Statistical Analysis

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“…Te UNH distribution is proposed by Shah et al [27]. Te probability density function of Nadarajah and Haghighi (NH) distribution is…”

Section: Unit Nadarajah and Haghighi Distributionmentioning

confidence: 99%

Max‐EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions

Akram

Ali

Shah

et al. 2022

Journal of Mathematics

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The recent industrial revolution is a result of modern technological advancement and industrial improvements require quick detection of assignable causes in a process. This study presents a monitoring scheme for unit interval data assuming beta and unit Nadarajah and Haghighi distributions. To this end, a maximum exponentially weighted moving average (Max-EWMA) chart is introduced to jointly monitor unit interval bounded time and magnitude data. The performance of the proposed chart is evaluated by using average run length and other characteristics of run length distribution using extensive Monte Carlo simulations. Besides a comprehensive simulation study, a real data set is also used to assess the performance of the chart. The results supplementing the proposed chart are efficient for joint monitoring time and magnitude, and simultaneous shifts are detected more quickly than separate shifts in the process parameters.

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Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

Bantan

Shafiq

Tahir

et al. 2022

Journal of Function Spaces

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In this paper, a new distribution named as unit-power Weibull distribution (UPWD) defined on interval (0,1) is introduced using an appropriate transformation to the positive random variable of the Weibull distribution. This work offers quantile function, linear representation of the density, ordinary and incomplete moments, moment-generating function, probability-weighted moments, L -moments, TL-moments, Rényi entropy, and MLE estimation. Additionally, several actuarial measures are computed. The real data applications are carried out to underline the practical usefulness of the model. In addition, a bivariate extension for the univariate power Weibull distribution named as bivariate unit-power Weibull distribution (BIUPWD) is also configured. To elucidate the bivariate extension, simulation analysis and application using COVID-19-associated fatality rate data from Italy and Belgium to conform a BIUPW distribution with visual depictions are also presented.

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Unit Nadarajah and Haghighi Distribution: Properties and Applications in Quality Control

Cited by 5 publications

References 25 publications

Study of a bounded interval perks distribution with quantile regression analysis

Study of a bounded interval perks distribution with quantile regression analysis

Max‐EWMA Chart Using Beta and Unit Nadarajah and Haghighi Distributions

Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model

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