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Table 9 Maximum likelihood estimates for Kevlar 49/epoxy strands failure times data (pressure at 70%)

From: The TR {Y} power series family of probability distributions

Distribution

GW*

BN*

GUWELOP

Parameter estimates

\( \hat{\alpha}=2.6948 \)

  (0.8101)

\( \hat{\gamma}=4.11091 \)

   (1.0456)

\( \hat{\beta}=1.3118 \)

   (0.5144)

\( \hat{\lambda}=6165.69 \)

  (1749.51)

\( \hat{a}=0.1626 \)

  (0.1039)

\( \hat{b}=0.1157 \)

   (0.0199)

\( \hat{\mu}=7826 \)

   (1759.97)

\( \hat{\sigma}=1339.35 \)

   (245.62)

\( \hat{\alpha}=2.0433 \)

  (0.8129)

\( \hat{\gamma}=3.6464 \)

   (1.9910)

\( \hat{\beta}=1.5924 \)

   (1.2346)

\( \hat{\lambda}=4546.90 \)

  (2220.66)

\( \hat{\theta}=-0.6017 \)

   (2.5271)

Log likelihood

−478.51

−480.52

−478.8681

AIC

965.0

969.0

967.7362

KS

p value

0.0749

0.9462

0.0797

0.9144

0.0703

0.9549

  1. (Standard error of estimates in parenthesis)
  2. *Maximum likelihood estimates, loglikelihood, AIC, KS statistic, and its p value of the GW and BN distributions were obtained from Al-Aqtash et al. [29]