Search Results for ""

Let S_n be the sum of n random variates X_i with a Bernoulli distribution with P(X_i=1)=p_i. Then sum_(k=0)^infty|P(S_n=k)-(e^(-lambda)lambda^k)/(k!)|<2sum_(i=1)^np_i^2, ...

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 ...

Quantile-quantile plots (also called q-q plots) are used to determine if two data sets come from populations with a common distribution. In such a plot, points are formed ...

The sequence of variates X_i with corresponding means mu_i obeys the strong law of large numbers if, to every pair epsilon,delta>0, there corresponds an N such that there is ...

Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). ...

A cadlag function is a function, defined on R or a subset of R, that is right continuous and has a left limit. The acronym cadlag comes from the French "continue à droite, ...

Dini's theorem is a result in real analysis relating pointwise convergence of sequences of functions to uniform convergence on a closed interval. For an increasing sequence ...

In real and functional analysis, equicontinuity is a concept which extends the notion of uniform continuity from a single function to collection of functions. Given ...

The orthogonal polynomials defined by h_n^((alpha,beta))(x,N)=((-1)^n(N-x-n)_n(beta+x+1)_n)/(n!) ×_3F_2(-n,-x,alpha+N-x; N-x-n,-beta-x-n;1) =((-1)^n(N-n)_n(beta+1)_n)/(n!) ...