Table 4 The ALC’s for credible intervals for \(NBS\left(\alpha ,\beta \right).\)

From: Birnbaum Saunders distribution for imprecise data: statistical properties, estimation methods, and real life applications

n

Credible intervals

\(NBS(\alpha ,\beta )\)

\(\left({\alpha }_{N},{\beta }_{N}\right)=\left(\mathrm{1.25,3}\right)\), \({I}_{N}=\left(\mathrm{0.2,0.5}\right)\)

ACL

Prior 1

Prior 2

Prior3

\({\alpha }_{N}\)

\({\beta }_{N}\)

\({\alpha }_{N}\)

\({\beta }_{N}\)

\({\alpha }_{N}\)

\({\beta }_{N}\)

50

(0.9299, 0.9450)

(0.9406, 0.9420)

(0.9321, 0.9329)

(0.9276, 0.9238)

(0.9286, 0.9295)

(0.9466, 0.9538)

100

(0.9389, 0.9391)

(0.9380, 0.9466)

(0.9435, 0.9446)

(0.9257, 0.9280)

(0.9465, 0.9473)

(0.9491, 0.9578)

200

(0.9362, 0.9387)

(0.9227, 0.9324)

(0.9513, 0.9542)

(0.9389, 0.9401)

(0.9584, 0.9586)

(0.9213, 0.9456)

500

(0.9402, 0.9419)

(0.9212, 0.9222)

(0.9391, 0.9579)

(0.9271, 0.9403)

(0.9464, 0.9540)

(0.9240, 0.9262)

\(\left({\alpha }_{N},{\beta }_{N}\right)=\left(\mathrm{0.5,3}\right)\), \({I}_{N}=\left(\mathrm{0.2,0.5}\right)\)

 50

(0.9322, 0.9518)

(0.9386, 0.9393)

(0.9433, 0.9478)

(0.9433, 0.9487)

(0.9400, 0.9441)

(0.9416, 0.9492)

 100

(0.9296, 0.9317)

(0.9338, 0.9344)

(0.9246, 0.9267)

(0.9339, 0.9468)

(0.9362, 0.9415)

(0.9353, 0.9392)

 200

(0.9192 0.9337)

(0.9228, 0.9234)

(0.9195, 0.9267)

(0.9446, 0.9461)

(0.9194, 0.9212)

(0.9402, 0.9520)

 500

(0.9402, 0.9417)

(0.9333, 0.9458)

(0.9333, 0.9437)

(0.9378, 0.9451)

(0.9307, 0.9341)

(0.9426, 0.9433)

\(\left({\alpha }_{N},{\beta }_{N}\right)=\left(\mathrm{1,3}\right)\), \({I}_{N}=\left(\mathrm{0.2,0.5}\right)\)

 50

(0.9146, 0.9203)

(0.9354, 0.9362)

(0.9471, 0.9485)

(0.9382, 0.9433)

(0.9323, .9335)

(0.9348, 0.9500)

 100

(0.9432, 0.9434)

(0.9339 0.9384)

(0.9363, 0.9364)

(0.9315, 0.9436)

(0.9247, 0.9406)

(0.9371, .9390)

 200

(0.9287, 0.9318)

(0.9293, 0.9301)

(0.9337, 0.9349)

(0.9377, 0.9404)

(0.9125, 0.9232)

(0.9362, 0.9349)

 500

(0.9349, 0.9394)

(0.9312, 0.9374)

(0.9262, 0.9320)

(0.9430, 0.9451)

(0.9313, 0.9340)

(0.9304, 0.9366)

\(\left({\alpha }_{N},{\beta }_{N}\right)=\left(\mathrm{1.25,3}\right)\), \({I}_{N}=\left(\mathrm{0.6,0.8}\right)\)

 50

(0.9443 0.9446)

(0.9301, 0.9409)

(0.9355, 0.9488)

(0.9285, 0.9293)

(0.9250, 0.9295)

(0.9457, 0.9576)

 100

(0.9250, 0.9316)

(0.9391, 0.9446)

(0.9356, 0.9423)

(0.9289, 0.9298)

(0.9407, 0.9462)

(0.9351, 0.9597)

 200

(0.9351, 0.9434)

(0.9265, 0.9274)

(0.9368, 0.9492)

(0.9443, 0.9457)

(0.9270, 0.9319)

(0.9314, 0.9409)

 500

(0.9382, 0.9439)

(0.9175, 0.9201)

(0.9325, 0.9344)

(0.9458, 0.9462)

(0.9418, 0.9434)

(0.9232, 0.9274)

\(\left({\alpha }_{N},{\beta }_{N}\right)=\left(\mathrm{0.5,3}\right)\), \({I}_{N}=\left(\mathrm{0.6,0.8}\right)\)

 50

(0.9314, 0.9323)

(0.9335, 0.9373)

(0.9249, 0.9380)

(0.9458, 0.9461)

(0.9370, 0.9378)

(0.9369, 0.9605)

 100

(0.9342, 0.9444)

(0.9416, 0.9420)

(0.9137, 0.9215)

(0.9470, 0.9482)

(0.9360, 0.9377)

(0.9344, 0.9394)

 200

(0.9309, 0.9318)

(0.9300, 0.9302)

(0.9162, 0.9204)

(0.9442, 0.9448)

(0.9163, 0.9222)

(0.9416, 0.9433)

 500

(0.9455, 0.9464)

(0.9471, 0.9484)

(2.9324, 2.9396)

(0.9245, 0.9375)

(0.9348, 0.9350)

(0.9394, 0.9443)

\(\left({\alpha }_{N},{\beta }_{N}\right)=\left(\mathrm{1,3}\right)\), \({I}_{N}=\left(\mathrm{0.6,0.8}\right)\)

 50

(0.9220, 0.9259)

(0.9456, 0.9464)

(0.9318, 0.9420)

(0.9238, 0.9366)

(0.9370, 0.9389)

(0.9381, 0.9433)

 100

(0.9523, 0.9524)

(0.9323, 0.9341)

(0.9178, 0.9249)

(0.9338, 0.9411)

(0.9287, 0.9410)

(0.9452, 0.9460)

 200

(0.9311, 0.9321)

(0.9314, 0.9321)

(0.9334, 0.9373)

(0.9373, 0.9446)

(0.9272, 0.9362)

(0.9328, 0.9352)

 500

(0.9383, 0.9420)

(0.9356, 0.9366)

(0.9335, 0.9347)

(0.9305, 0.9405)

(0.9381, 0.9465)

(0.9403, 0.9429)

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