Description Usage Arguments Details Value Author(s) References See Also Examples
The function provides sample estimates of reliability of stress-strength models, where stress and strength are modeled as independent r.v., whose distribution form is known except for the values of its parameters, assumed all unknown
1 |
x |
a random sample from r.v. X modeling strength |
y |
a random sample from r.v. Y modeling stress |
family |
the distribution of both X and Y |
twoside |
if TRUE, the function computes two-side confidence intervals; otherwise, one-side (a lower bound) |
type |
type of confidence interval (CI) to be built. For the normal family, "RG" stands for Reiser-Guttman, "AN" for large sample (asymptotically normal), "LOGIT" or "ARCSIN" for logit or arcsin variance stabilizing tranformations, "B" for percentile bootstrap, "GK" for Guo-Krishnamoorthy (one-sided only). |
alpha |
the complement to one of the nominal confidence level |
B |
number of bootstrap replicates (for type "B") |
For more details, please have a look at the references listed below
A list comprising
ML_est |
the sample value of the maximum likelihood estimator; for normal r.v. \hat{R}=Φ[(\bar{x}-\bar{y})/√{\hat{σ}_x^2+\hat{σ}_y^2}], where \bar{x} and \bar{y} are the sample means, and \hat{σ}_x^2, \hat{σ}_y^2 the biased maximum likelihood variance estimators |
Downton_est |
(for normal r.v.) the sample value of one of the approximated UMVU estimators proposed by Downton \hat{R}'=Φ[(\bar{x}-\bar{y})/√{s_x^2+s_y^2}] |
CI |
the confidence interval |
confidence_level |
the nominal confidence level 1-α |
Alessandro Barbiero, Riccardo Inchingolo
Barbiero A (2011) Confidence Intervals for Reliability of Stress-Strength Models in the Normal Case, Comm Stat Sim Comp 40(6):907-925
Downton F. (1973) The Estimation of Pr (Y < X) in the Normal Case, Technometrics , 15(3):551-558
Kotz S, Lumelskii Y, Pensky M (2003) The stress-strength model and its generalizations: theory and applications. World Scientific, Singapore
Guo H, Krishnamoorthy K (2004) New approximate inferential methods for the reliability parameter in a stress-strength model: The normal case. Commun Stat Theory Methods 33:1715-1731
Mukherjee SP, Maiti SS (1998) Stress-strength reliability in the Weibull case. Frontiers In Reliability 4:231-248. WorldScientific, Singapore
Reiser BJ, Guttman I (1986) Statistical inference for P(Y<X): The normal case. Technometrics 28:253-257
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | # distributional parameters of X and Y
parx<-c(1, 1)
pary<-c(0, 2)
# sample sizes
n<-10
m<-20
# true value of R
SSR(parx,pary)
# draw independent random samples from X and Y
x<-rnorm(n, parx[1], parx[2])
y<-rnorm(m, pary[1], pary[2])
# build two-sided confidence intervals
estSSR(x, y, type="RG")
estSSR(x, y, type="AN")
estSSR(x, y, type="LOGIT")
estSSR(x, y, type="ARCSIN")
estSSR(x, y, type="B")
estSSR(x, y, type="B",B=1000) # change number of bootstrap replicates
# and one-sided
estSSR(x, y, type="RG", twoside=FALSE)
estSSR(x, y, type="AN", twoside=FALSE)
estSSR(x, y, type="LOGIT", twoside=FALSE)
estSSR(x, y, type="ARCSIN", twoside=FALSE)
estSSR(x, y, type="B", twoside=FALSE)
estSSR(x, y, type="GK", twoside=FALSE)
# changing sample sizes
n<-20
m<-30
x<-rnorm(n, parx[1], parx[2])
y<-rnorm(m, pary[1], pary[2])
# build tow-sided confidence intervals
estSSR(x, y, type="RG")
estSSR(x, y, type="AN")
estSSR(x, y, type="LOGIT")
estSSR(x, y, type="ARCSIN")
estSSR(x, y, type="B")
|
[1] 0.6726396
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
[1] 0.3673573 0.7281561
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
[1] 0.3689178 0.7294760
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
[1] 0.3690406 0.7267037
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
[1] 0.3685168 0.7337505
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
2.5% 97.5%
0.3612767 0.7531282
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
2.5% 97.5%
0.3638068 0.7440848
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
[1] 0.3963499
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
[1] 0.3979414
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
[1] 0.3978083
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
[1] 0.3979228
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
5%
0.3913651
$confidence_level
[1] 0.95
$ML_est
[1] 0.5549802
$Downton_est
[1] 0.5533748
$CI
[1] 0.3935198
$confidence_level
[1] 0.95
$ML_est
[1] 0.472842
$Downton_est
[1] 0.4733472
$CI
[1] 0.3286397 0.6217025
$confidence_level
[1] 0.95
$ML_est
[1] 0.472842
$Downton_est
[1] 0.4733472
$CI
[1] 0.3281845 0.6212163
$confidence_level
[1] 0.95
$ML_est
[1] 0.472842
$Downton_est
[1] 0.4733472
$CI
[1] 0.3294962 0.6208098
$confidence_level
[1] 0.95
$ML_est
[1] 0.472842
$Downton_est
[1] 0.4733472
$CI
[1] 0.3263167 0.6218000
$confidence_level
[1] 0.95
$ML_est
[1] 0.472842
$Downton_est
[1] 0.4733472
$CI
2.5% 97.5%
0.3100088 0.6311439
$confidence_level
[1] 0.95
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