

Chisquare {base}                             R Documentation

_T_h_e _(_n_o_n_-_c_e_n_t_r_a_l_) _C_h_i_-_S_q_u_a_r_e _D_i_s_t_r_i_b_u_t_i_o_n

_U_s_a_g_e_:

     dchisq(x, df, ncp=0)
     pchisq(q, df, ncp=0)
     qchisq(p, df, ncp=0)
     rchisq(n, df)

_A_r_g_u_m_e_n_t_s_:

     x,q: vector of quantiles.

       p: vector of probabilities.

       n: number of observations to generate.

      df: degrees of freedom.

     ncp: non-centrality parameter.

_V_a_l_u_e_:

     These functions provide information about the chi-
     square (chi^2) distribution with `df' degrees of free-
     dom and optional non-centrality parameter `ncp'.

     The chi-square distribution with `df'= n degrees of
     freedom has density

      f_n(x) = 1 / (2^(n/2) Gamma(n/2))  x^(n/2-1) e^(-x/2)

     for x > 0. Mean and variance are n and 2n, respec-
     tively.

     `dchisq' gives the density f_n, `pchisq' gives the dis-
     tribution function F_n, `qchisq' gives the quantile
     function and `rchisq' generates random deviates.

     The non-central chi-square distribution with `df'= n
     degrees of freedom and non-centrality parameter `ncp' =
     lambda has density

          f(x) = exp(-lambda/2) SUM_{r=0}^infty ((lambda/2)^r / r!) dchisq(x, df + 2r)

     for x >= 0.

_S_e_e _A_l_s_o_:

     `dgamma' for the gamma distribution which generalizes
     the chi-square one.

_E_x_a_m_p_l_e_s_:

     dchisq(1, df=1:3)
     pchisq(1, df= 3)
     pchisq(1, df= 3, ncp = 0:4)# includes the above

     x <- 1:10
     ## Chisquare( df = 2) is a special exponential distribution
     all.equal(dchisq(x, df=2), dexp(x, 1/2))
     all.equal(pchisq(x, df=2), pexp(x, 1/2))

