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Table 1 Summary of some special cases of the BEF(θ012;c) or BIEF(β012;c)

From: Bivariate general exponential models with stress-strength reliability application

DistributionBEF(θ0, θ1, θ2; c)BIEF(β0, β1, β2; c)R
θig1(x; c)βig2(x; c)
M-O bivariate exponentialθix__\( \frac{\theta_2}{\theta_0+{\theta}_1+{\theta}_2} \), see [7]
Bivariate Rayleighλix2__\( \frac{\lambda_2}{\lambda_0+{\lambda}_1+{\lambda}_2} \), see [9]
M-O bivariate Weibull\( \frac{1}{{\theta_i}^c} \)xc__\( \frac{\theta_0^c{\theta}_1^c}{\theta_0^c+{\theta}_1^c+{\theta}_2^c} \)
M-O Paretoai\( \ln \left(\frac{x}{c}\right) \)__\( \frac{a_2}{a_0+{a}_1+{a}_2} \)
Bivariate inverse Weibull__\( \frac{1}{{\theta_i}^c} \)xc\( \frac{\theta_0^c{\theta}_2^c}{\theta_0^c+{\theta}_1^c+{\theta}_2^c} \)
Bivariate Burr type III__bi\( \ln \left(\frac{1+{x}^c}{x^c}\right) \)\( \frac{b_1}{b_0+{b}_1+{b}_2} \)