mark@elsie.UUCP (12/06/83)
I need a reference to what should be a rather common problem in statistics. What is the probability of finding m events in N tries where the probability of an event is given by p(i), where 0 <= i <= m <= N, and p(i) <= p(i+1). That is, the probability of an event is a function of the number of previous successes, and , in general, that probability decreases with each success. For example: if we have a number of balls, B of which r are red and b are blue (r+b = B), what is the probability of picking out m red balls (m <= r) in N tries where each RED ball is discarded after it is picked and the BLUE balls are returned to the pile. I recognize that the binomial distribution is applicable in the case where the probability of an event remains constant, but in this case, the probability decreases. I've worked out an approximate solution, based on the binomial distribution, that is close enough for the program I've written. But I haven't been able to find a reference to this problem in any of the standard references I'm capable of understanding (Knuth; Snedecor & Cochran; etc.). I need to reference this stuff in a biologically oriented paper (I'm a biochemist by training), and I don't want to try to include the proof in same (Dear Dr. Miller, We don't feel this paper is appropriate for our journal, try the ACM.). Also, I don't want to reproduce something that was probably done by some German in the late 18th century. Feel free to reply either directly or over net.math. Thanx in advance. -- UUCP: decvax!harpo!seismo!rlgvax!cvl!elsie!mark Phone: (301) 496-5688
emigh@ecsvax.UUCP (12/07/83)
Reference: Poisson, Simeon Denis (1837). Recherches sur la Probabilite des Jugements en Matiere Criminelle et en Matiere Civile, Precedees des Regles Generales du Calcul des Probabilities. Bachelier, Imprimeur-Libraire pour les Mathematiques, la Physique, etc. Paris. No distribution is given, but the mean and variance are calculated. A more modern reference for this is: Johnson, Norman L. and Samuel Kotz (1969). Distributions in Statistics: Discrete Distributions. Wiley, New York. (They also have volumes on Continuous Univariate Distributions and Multivariate Distributions). --Ted H. Emigh/Depts of Genetics and Statistics/NCSU ...decvax!duke!unc!ecsvax!emigh