On the Limiting Form of the Contagious Binomial Distribution And Its Applicati
On the Limiting Form of the Contagious Binomial Distribution And Its Applicati
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Of X = i/N when N -► «> in such a way that X = i/N remains constant. That is, where C indicates that X = i/N remains constant, lim h{x) = lim N p(x) -^ f(X) N -» oo N-» oo X=(i/N)^C X=(i/N)=C (3) Page 8.
Thus (3) gives the function which must be taken to the limit in order to obtain the probability density function of X, f(X).
For any fixed N, there is a direct equivalence between p(X) in (3) and the p given by (2). Clearly, for some fixed N, the event X = i/N occurs if, and only if, the event ...i occurs. Hence for fixed N the events X = i/N and i are equivalent and consequently they have the same probability of occurrence. Thus p(X=i/N) = p, . But the steady-state distribution of i for some fixed N has been given in (2) . Hence (3) may be written as f (x) = lira N p. .^s i/N=C = lim t^Tum r(f) r(N+^) r(^) A result on the limiting behavior of gamma functions when a term in the gamma argument increases without limit is needed if the limit on the right hand side of (4) is to be found.
What to read after On the Limiting Form of the Contagious Binomial Distribution And Its Applicati?
You can find similar books in the "Read Also" column, or choose other free books by David Bruce Montgomery to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Of X = i/N when N -► «> in such a way that X = i/N remains constant. That is, where C indicates that X = i/N remains constant, lim h{x) = lim N p(x) -^ f(X) N -» oo N-» oo X=(i/N)^C X=(i/N)=C (3) Page 8.
Thus (3) gives the function which must be taken to the limit in order to obtain the probability density function of X, f(X).
For any fixed N, there is a direct equivalence between p(X) in (3) and the p given by (2). Clearly, for some fixed N, the event X = i/N occurs if, and only if, the event ...i occurs. Hence for fixed N the events X = i/N and i are equivalent and consequently they have the same probability of occurrence. Thus p(X=i/N) = p, . But the steady-state distribution of i for some fixed N has been given in (2) . Hence (3) may be written as f (x) = lira N p. .^s i/N=C = lim t^Tum r(f) r(N+^) r(^) A result on the limiting behavior of gamma functions when a term in the gamma argument increases without limit is needed if the limit on the right hand side of (4) is to be found.
What to read after On the Limiting Form of the Contagious Binomial Distribution And Its Applicati?
You can find similar books in the "Read Also" column, or choose other free books by David Bruce Montgomery to read onlineMoreLess
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