TY - JOUR
T1 - On the maximum and minimum for classes of univariate distributions
AU - Nadarajah, S.
AU - Okorie, I. E.
N1 - Funding Information:
The authors would like to thank the Editor and the three referees for careful reading and comments which greatly improved the paper.
Publisher Copyright:
© 2021, The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.
PY - 2021/4
Y1 - 2021/4
N2 - Given a random sample X1, X2, … , Xn, the distributions of min (X1, X2, … , Xn) and max (X1, X2, … , Xn) are of interest in many areas. We derive explicit expressions for moments of min (X1, X2, … , Xn) and max (X1, X2, … , Xn) for thirty four families of distributions, including the normal and Student’s t distributions. These results can be especially useful when data are scarce. The correctness of the expressions is checked by a simulation study. Applications to two engineering data sets are given.
AB - Given a random sample X1, X2, … , Xn, the distributions of min (X1, X2, … , Xn) and max (X1, X2, … , Xn) are of interest in many areas. We derive explicit expressions for moments of min (X1, X2, … , Xn) and max (X1, X2, … , Xn) for thirty four families of distributions, including the normal and Student’s t distributions. These results can be especially useful when data are scarce. The correctness of the expressions is checked by a simulation study. Applications to two engineering data sets are given.
KW - Moments
KW - Normal distribution
KW - Student’s t distribution
UR - http://www.scopus.com/inward/record.url?scp=85102314324&partnerID=8YFLogxK
U2 - 10.1007/s13198-021-01078-y
DO - 10.1007/s13198-021-01078-y
M3 - Article
AN - SCOPUS:85102314324
SN - 0975-6809
VL - 12
SP - 290
EP - 309
JO - International Journal of System Assurance Engineering and Management
JF - International Journal of System Assurance Engineering and Management
IS - 2
ER -
