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A theorem proved by Doob (1942) which states that any random process which is both normal and Markov has the following forms for its correlation function C_y(tau), spectral ...

If the random variates X_1, X_2, ... satisfy the Lindeberg condition, then for all a<b, lim_(n->infty)P(a<(S_n)/(s_n)<b)=Phi(b)-Phi(a), where Phi is the normal distribution ...

The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the (2+epsilon)th moment (with epsilon>0) exists for a statistical distribution of ...

The term "range" has two completely different meanings in statistics. Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j, the range of the random sample ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...

Let the absolute frequencies of occurrence of an event in a number of class intervals be denoted f_1, f_2, .... The cumulative frequency corresponding to the upper boundary ...

There are infinitely many primes m which divide some value of the partition function P.

The grouping of data into bins (spaced apart by the so-called class interval) plotting the number of members in each bin versus the bin number. The above histogram shows the ...

The function z=f(x)=ln(x/(1-x)). (1) This function has an inflection point at x=1/2, where f^('')(x)=(2x-1)/(x^2(x-1)^2)=0. (2) Applying the logit transformation to values ...

Given two paired sets X_i and Y_i of n measured values, the paired t-test determines whether they differ from each other in a significant way under the assumptions that the ...