TY - JOUR
T1 - A note on the stability of the estimation of the exponential distribution
AU - Baxter, Laurence A.
AU - Rachev, Svetlozar T.
N1 - Funding Information:
Research supported by the Air Force Office of Scientific Research, AFSC, USAF, under grant AFOSR-86-0136. The US Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. * Present address: Statistics and Applied Probability Program, University of California, Santa Barbara, CA 93106, USA.
PY - 1990/6
Y1 - 1990/6
N2 - Bounds on the uniform distance between a χ22n distribution and the distribution of 2Σni = 1 Xi/μ, where X1, X2,..., Xn are n independent, identically distributed nonnegative random variables with common mean μ, are derived assuming that the Xi's are HNBUE or HNWUE or that a specific 'mechanism' is 'perturbing' an exponential distribution. These bounds are used to quantify the robustness of the sampling distribution of the usual test statistic for hypothesis tests on the mean of the exponential distribution to departures from exponentiality.
AB - Bounds on the uniform distance between a χ22n distribution and the distribution of 2Σni = 1 Xi/μ, where X1, X2,..., Xn are n independent, identically distributed nonnegative random variables with common mean μ, are derived assuming that the Xi's are HNBUE or HNWUE or that a specific 'mechanism' is 'perturbing' an exponential distribution. These bounds are used to quantify the robustness of the sampling distribution of the usual test statistic for hypothesis tests on the mean of the exponential distribution to departures from exponentiality.
KW - Exponential distribution
KW - HNBUE
KW - HNWUE
KW - chi-square distribution
KW - probability metric
KW - robustness
KW - stability theory
UR - http://www.scopus.com/inward/record.url?scp=45149137874&partnerID=8YFLogxK
U2 - 10.1016/0167-7152(90)90109-K
DO - 10.1016/0167-7152(90)90109-K
M3 - Article
AN - SCOPUS:45149137874
SN - 0167-7152
VL - 10
SP - 37
EP - 41
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
IS - 1
ER -