Downloaded from https://www.everyspec.com AMCP 706196 The s-confidence level associated with a poifc(k; A) - 1fh{k, "f1o range" usually will be roughly 5O'%- 80%, (the s-normnl tables will not give a .. correct answer). Example No, 2 illhstrtes " U A) (2-20a) the procedure for obtaining s-.onfidence The of1' tAnd polfc In Eq. 2.20 can be ex- 2.3.2 POISSON premed In torms of the chlisquare Cdf and Sf, cvqf and 'aqic.
(See Part Six, Mathe.- The discrete random variable k is the num.- ath'al Appendix ant Glossary.) ber of events which occur in a fixed set of circumstances, Examples are the number of poifv(hk 0) - cSqf(0 p 2k) (2-2La) defects in 3.5 yd' of cloth, the number of failuvas during a 2-hr test, and the number poif (A 1 Ip) - vaqfc(2$A 2h + 2) (2-21b) of accidents per driver in 10 yr. If the 'Irnlts. variable k has the Poisson distribution, the The mean and variance are prou.aa that nnerates k is often called a Poisson proctus.
In a Polison process, it Is {k} - p (2-221) -ometimas convenient to define a rate param- 1etr, e,.,, the number of defects per square Var { u} - P (2-22b) yard of cloth, the number of failures par hour, or the number of failures per driver The usual stntistital problem is to estimate per year, p. The Poisson distribution often is used as an approximation to the binomial distribution Use the following notation: with pol* base-name for Poisson distribution, P (2-23) the * is replaced by ,n to denote the pnf, by f to denote the Cdf, and thus the statistical problem may be to or by f' to denote the Sf estimate p. Vq.
2-23 is satisfactory for N large (say, N > 10) and 1) Niall (say, k - number o1 events which occur p 0.1), and even works roasonably well (must be a non-negative integer) when those conditions are violated. p * mean numb r of' events The maximum likelihood, unbiased esti- "mate A of ) Is "The probability mass function prnf, the Cd' and SY are =k (2-24) pobn(k •,u) "pnMfjk; J} Calculating s-confidmn,-e limits for m is more complicated than when the random , Oxp (-. p)IA/kl (2-20a) variable is continuous.
A good explanation is given in Part Six, Mathematical Appendix pof W, pA) - Cdf {k; p) and Glossary, 2-sided s-confidence state- iments for I are of the form - 2, pomiM 4 J) (2-20b) CoV1f{M, J , 1 A,} 1, A (2-5a) ' , I I I II I