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

VL - 10

SP - 37

EP - 41

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 1

ER -