Statistical Analysis With Missing Data (Wiley Series in by Roderick J. A. Little

By Roderick J. A. Little

Said specialists at the topic assemble different resources on tools for statistical research of information units with lacking values, a pervasive challenge for which usual tools are of restricted worth. mixing concept and alertness, it reports ancient ways to the topic, and rigorous but easy equipment for multivariate research with lacking values. is going directly to supply a coherent thought for research of difficulties in keeping with likelihoods derived from statistical types for the information and the lacking facts mechanism. the speculation is utilized to quite a lot of very important missing-data difficulties. huge references, examples, and workouts.

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Additional info for Statistical Analysis With Missing Data (Wiley Series in Probability and Statistics)

Example text

Assume that the intrinsic growth rate r(N) includes a resource recovery time of one time interval, and is logistic in nature; thus let -45- a. b. c. Determine the stability of the equilibrium at N = K. For convenience, let 6t = T. Make a plot of the root(s) of the Characteristic Equation in the complex plane, clearly illustrating the regions of stability and instability. Compare the results of the above model with those found earlier for the discrete time logistic equation without explicit time delays.

Note that this method can be used with the Pure Birth Process too. (t). 1 Note that the sum runs over all possible population sizes. Although we will assume the population initially numbers j at t = 0, so that E(N) = j at t = 0, since deaths can occur as well as births, the possibility of a population size smaller than j at times t > 0 does not vanish. b. simplify notation: PN(t) PN) dEd(tN) = L {-(A+~)i2p. 2 I.. 2 . -lPi+1Pi-I-1Pi_1 ) y i=l and by redefining the indices in the summations, 00 dE(N) = A I Pk{- k 2 + (k+I)2 - (k+l)) dt k=O 00 - ~ I Pk{k 2 - (k-l) 2 - (k-l)} k=O 00 = A I k=O 00 kPk - ~ L k=O kPk = (A-~)E(N).

6119. 092. It is possible to interpret our approximate result quite generally. Q,n R > 0, thus Prob{extinction} O. -+ In other words, the probability that the population becomes eventually extinct or grows without bound depends upon whether the true mean of the logarithm of the random variable R is negative or positive. On the other hand, the expected population size eventually becomes extinct or grows without bound according to whether the true mean of the random variable R itself, is less than or greater than unity.

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