Downloaded from https://www.everyspec.com AMCP 706198 tc the following notation: b2 is the maximum likelihood estimate for 02.The unbiased estimate s2 for the var- JA mnean (location pnrameter) ance 0a is n standartd deviation O(cal, prameter) ,2 ,. Ч (2 N-) a (2-34) The s-statistic in Eq. 2-34 is also very useful N'vr s alllphf.
siWin many statistical tests InvolvihM the s-nonmal distribution; s is NOT an unbiased estimator .j - Valhic of X for item i In sample for a, The good reason s is used so much, rather than &, is that the sampling distribu- The pcI' and ('dr arl tion of s Is known well, whereas that of b is nolt x~ rai-diy va-iabl- PdJx•'• o 2\ V / The Cdf of Y" is S(2-31a) Cdf R , JA U1o fflauf( '..35 CVddx {,•t (( ga,,f--- (2-3)b) 'rhe Cdf of s is P alld o froiln a s8,m1!1l1C Cdf{ f; ti } a, cuqf I (- iJ Ihe usual statistical prohlem, Is to estinmlte Us1 1 It is convenient to classify experiments (2-36) according to whether or not tile complete Isample wa Iakd, Eq.
2-35 is not feasible to us because a is not known, The Student t-di•trihution is 2-3,4,1 All Itens Tested to Failure used instead (see Ref. 30). "iThe maxiunoi likelihood, unbiased hsti- mate k of P is I/v has the Student ,-distribution with N - 1 degrees of freedom N pt sntuple mentnr Y (11N) Ex(2t7 lit (2,-37) (2-32) Example No, 9 Illustrates the application of' the Student W-distribution, "Thie sam1inple Inedhin is llso a[ very good esti, millate ol 1. 2-3.4.2 Censored Samples 'Ihliv maximum likelihood estimate for the Tle simple approach in par. 2-3,4.1 cannot shtndard deviation is the sample standard be used for censored samples.
Maximum deviation, likelihood inethods are most usual for estl- mation in this case and canl give an Idea of 1A/2 the uncertainties involved, Part Six or Ref. 0 1 (XI- ) (2-33) 13 or ia progranuner/stiitisticlan ought to be ''. S...............................