On a bivariate Kumaraswamy type exponential distribution

Mirhosseini, Seyed Mohsen; Dolati, Ali; Amini, Mohammad

doi:10.1080/03610926.2014.944664

Cited by 3 publications

(7 citation statements)

References 13 publications

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“…(IV) Bivariate Kumaraswamy type exponential distribution Mirhosseini et al 9 𝑔 𝐵𝐾𝐸 (𝑥 1 , 𝑥 2 ; 𝜆 1 , 𝜆 2 , 𝛼) = (28)…”

Section: (Ii) Bivariate Cubic Rayleigh Distributionmentioning

confidence: 99%

“…Akhter and Hirari 13 have defined this distribution as

\begin{equation}{g_{FGMR1}}\;\left( {{x_1},{x_2};\;\alpha ,\;\theta } \right) = \frac{{{{\rm{e}}^{ - \frac{{x_1^2 + x_2^2}}{{{\alpha ^2}}}}}{x_1}{x_2}\left( { - 2\left( { - 2 + {{\rm{e}}^{\frac{{x_1^2}}{{2{\alpha ^2}}}}}} \right)\theta + {{\rm{e}}^{\frac{{x_2^2}}{{2{\alpha ^2}}}}}\left( { - 2\theta + {{\rm{e}}^{\frac{{x_1^2}}{{2{\alpha ^2}}}}}\left( {1 + \theta } \right)} \right)} \right)}}{{{\alpha ^4}}}\;\end{equation}

where x 1,

{x_2} \ge 0,\;\alpha &gt; 0,\; - 1 \le \theta \le 1

. Bivariate Kumaraswamy type exponential distribution Mirhosseini et al 9

\begin{equation}{g_{BKE}}\;\left( {{x_1},{x_2};\;{\lambda _1},{\lambda _2},\alpha } \right) = \end{equation}

λ_{1} λ_{2} α e^{- ((), λ_{1} x_{1} + λ_{2} x_{2})} ([], 1 - α ((), 1 -))

…”

Section: Covid‐19 Applicationmentioning

confidence: 99%

“…Bivariate Kumaraswamy type exponential distribution Mirhosseini et al 9

\begin{equation}{g_{BKE}}\;\left( {{x_1},{x_2};\;{\lambda _1},{\lambda _2},\alpha } \right) = \end{equation}

\begin{equation*}{\lambda _1}{\lambda _2}\alpha {e^{ - \left( {{\lambda _1}{x_1} + {\lambda _2}{x_2}} \right)}}\left[ {1 - \alpha \left( {1 - {e^{ - {\lambda _1}{x_1}}}} \right)\left( {1 - {e^{ - {\lambda _2}{x_2}}}} \right)} \right]{\left[ {1 - \left( {1 - {e^{ - {\lambda _1}{x_1}}}} \right)\left( {1 - {e^{ - {\lambda _2}{x_2}}}} \right)} \right]^{\alpha - 2}}\end{equation*}

…”

Section: Covid‐19 Applicationmentioning

confidence: 99%

“…where, 𝐹(𝑥) is the baseline cumulative distribution and 𝐺(𝑥) is the generated cumulative distribution by using PHR model. There are more constructed models for PHR and PRHR in bivariate case; for example; Kundu and Gupta, 8 Mirhosseini et al, 9 and Sankaran and Gleeia. 10 Starting from the baseline univariate cumulative distributions 𝐹 1 (𝑥) and 𝐹 2 (𝑦), PHR model has been proposed in bivariate case as…”

Section: Introductionmentioning

confidence: 99%

“…There are more constructed models for PHR and PRHR in bivariate case; for example; Kundu and Gupta, 8 Mirhosseini et al., 9 and Sankaran and Gleeia. 10 …”

Section: Introductionmentioning

confidence: 99%

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Structure of bivariate Rayleigh proportional hazard rate model with its associated copula applied on COVID‐19 data

Hassanein

Seyam

2022

Quality & Reliability Eng

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Visualizing the fatality of coronavirus is a very tricky point through the world. In this paper, a new construction via the proportional hazard rate model with Rayleigh marginal is introduced and applied on COVID‐19 data set. The statistical and reliability characteristics of bivariate Rayleigh proportional hazard (BRPH) distribution are derived. The copula dependence structure and its properties are studied. The point estimation of the marginal and dependence parameters is introduced via maximum likelihood, method of moments, and inference function for margins (IFM) method. A simulation study is carried out to examine the effectiveness and the performance of the parameter estimates. Finally, an application on COVID‐19 data is used in a comparison study between BRPH model and other constructed bivariate models. This application concerned with modeling the fatality on COVID‐19. Throughout the results of goodness‐of‐fit criteria, BRPH provides a better fit than different competitors constructed bivariate models which reflects its flexibility and applicability on modeling the fatality of COVID‐19.

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“…(IV) Bivariate Kumaraswamy type exponential distribution Mirhosseini et al 9 𝑔 𝐵𝐾𝐸 (𝑥 1 , 𝑥 2 ; 𝜆 1 , 𝜆 2 , 𝛼) = (28)…”

Section: (Ii) Bivariate Cubic Rayleigh Distributionmentioning

confidence: 99%

“…Akhter and Hirari 13 have defined this distribution as

\begin{equation}{g_{FGMR1}}\;\left( {{x_1},{x_2};\;\alpha ,\;\theta } \right) = \frac{{{{\rm{e}}^{ - \frac{{x_1^2 + x_2^2}}{{{\alpha ^2}}}}}{x_1}{x_2}\left( { - 2\left( { - 2 + {{\rm{e}}^{\frac{{x_1^2}}{{2{\alpha ^2}}}}}} \right)\theta + {{\rm{e}}^{\frac{{x_2^2}}{{2{\alpha ^2}}}}}\left( { - 2\theta + {{\rm{e}}^{\frac{{x_1^2}}{{2{\alpha ^2}}}}}\left( {1 + \theta } \right)} \right)} \right)}}{{{\alpha ^4}}}\;\end{equation}

where x 1,

{x_2} \ge 0,\;\alpha &gt; 0,\; - 1 \le \theta \le 1

. Bivariate Kumaraswamy type exponential distribution Mirhosseini et al 9

\begin{equation}{g_{BKE}}\;\left( {{x_1},{x_2};\;{\lambda _1},{\lambda _2},\alpha } \right) = \end{equation}

λ_{1} λ_{2} α e^{- ((), λ_{1} x_{1} + λ_{2} x_{2})} ([], 1 - α ((), 1 -))

…”

Section: Covid‐19 Applicationmentioning

confidence: 99%

“…Bivariate Kumaraswamy type exponential distribution Mirhosseini et al 9

\begin{equation}{g_{BKE}}\;\left( {{x_1},{x_2};\;{\lambda _1},{\lambda _2},\alpha } \right) = \end{equation}

\begin{equation*}{\lambda _1}{\lambda _2}\alpha {e^{ - \left( {{\lambda _1}{x_1} + {\lambda _2}{x_2}} \right)}}\left[ {1 - \alpha \left( {1 - {e^{ - {\lambda _1}{x_1}}}} \right)\left( {1 - {e^{ - {\lambda _2}{x_2}}}} \right)} \right]{\left[ {1 - \left( {1 - {e^{ - {\lambda _1}{x_1}}}} \right)\left( {1 - {e^{ - {\lambda _2}{x_2}}}} \right)} \right]^{\alpha - 2}}\end{equation*}

…”

Section: Covid‐19 Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…There are more constructed models for PHR and PRHR in bivariate case; for example; Kundu and Gupta, 8 Mirhosseini et al., 9 and Sankaran and Gleeia. 10 …”

Section: Introductionmentioning

confidence: 99%

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