Table 4 The BEs and PRs under PLF with parameters \(\lambda_{1} = 0.4, \, \lambda_{2} = 0.3, \, \lambda_{3} = 0.2, \, p_{1} = 0.5, \, p_{2} = 0.3.\)

From: The 3-component mixture of power distributions under Bayesian paradigm with application of life span of fatigue fracture

\(t\)

\(n\)

Priors

BEs

\(\hat{\lambda }_{1}\)

\(\hat{\lambda }_{2}\)

\(\hat{\lambda }_{3}\)

\(\hat{p}_{1}\)

\(\hat{p}_{2}\)

00.9

30

UP

0.473699

0.392311

0.305913

0.490801

0.313692

JP

0.438033

0.363620

0.260598

0.491943

0.313734

IP

0.454581

0.374621

0.244704

0.478091

0.309406

50

UP

0.440035

0.357303

0.252612

0.494011

0.309304

JP

0.422166

0.334364

0.229331

0.494023

0.309486

IP

0.431558

0.351277

0.238926

0.48492

0.307309

100

UP

0.419892

0.325579

0.223074

0.497226

0.304248

JP

0.412053

0.314160

0.219033

0.498013

0.304786

IP

0.407296

0.318637

0.22410

0.487496

0.297906

\(t\)

\(n\)

Priors

PRs

00.9

30

UP

0.028845

0.038201

0.040083

0.015539

0.020761

JP

0.028336

0.037192

0.039420

0.015563

0.020797

IP

0.027668

0.035907

0.038064

0.014211

0.018355

50

UP

0.016763

0.021748

0.021856

0.009720

0.013170

JP

0.016717

0.021648

0.021716

0.009723

0.013189

IP

0.016634

0.020992

0.021519

0.009087

0.012122

100

UP

0.007254

0.011063

0.009877

0.005781

0.006787

JP

0.007116

0.011043

0.009716

0.005793

0.006799

IP

0.006623

0.009812

0.010062

0.002167

0.002596