Table 7 The BEs and PRs under QLF 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

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

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

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

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

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

00.6

30

UP

0.415721

0.252012

0.155527

0.412341

0.231452

JP

0.437801

0.244725

0.148792

0.415782

0.239854

IP

0.438952

0.250868

0.150901

0.405271

0.256971

50

UP

0.410216

0.268754

0.170264

0.438427

0.246923

JP

0.368754

0.250011

0.165734

0.431798

0.250314

IP

0.371548

0.257467

0.170012

0.420122

0.260341

100

UP

0.398754

0.287906

0.185954

0.462346

0.268917

JP

0.370241

0.275914

0.176458

0.469867

0.269898

IP

0.379985

0.280347

0.180647

0.450012

0.278142

\(t\)

\(n\)

Priors

PRs

00.6

30

UP

0.389534

0.47132

0.52641

0.152346

0.268674

JP

0.412567

0.511230

0.665234

0.167714

0.280122

IP

0.365491

0.442657

0.547889

0.123645

0.219850

50

UP

0.302145

0.387564

0.402651

0.112340

0.185501

JP

0.324598

0.425661

0.445620

0.123324

0.193325

IP

0.268746

0.356001

0.378991

0.109875

0.166887

100

UP

0.187564

0.275694

0.359870

0.075688

0.1234560

JP

0.200344

0.299810

0.376900

0.098860

0.168985

IP

0.142354

0.246010

0.293312

0.046772

0.102360