SkewLaplace              package:rmutil              R Documentation

_S_k_e_w _L_a_p_l_a_c_e _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     These functions provide information about the skew Laplace
     distribution with location parameter equal to 'm', dispersion
     equal to 's', and skew equal to 'f': density, cumulative
     distribution, quantiles, log hazard, and random generation. For
     'f=1', this is an ordinary (symmetric) Laplace distribution.

     The skew Laplace distribution has density

                 f(y) = f*exp(-f*(y-m)/s)/((1+f^2)*s)

     if  y>=m and else

                f(y) = f*exp((y-m)/(f*s))/((1+f^2)*s)

     where m is the location parameter of the distribution, s is the
     dispersion, and f is the skew.

     The mean is given by m + (s * (1 - f^2)) / (sqrt(2) * f) and the
     variance by  (s^2 * (1 + f^4)) / (2 * f^2).

     Note that this parametrization of the skew (family) parameter is
     different than that used for the multivariate skew Laplace
     distribution in 'elliptic'.

_U_s_a_g_e:

     dskewlaplace(y, m=0, s=1, f=1, log=FALSE)
     pskewlaplace(q, m=0, s=1, f=1)
     qskewlaplace(p, m=0, s=1, f=1)
     hskewlaplace(y, m=0, s=1, f=1)
     rskewlaplace(n, m=0, s=1, f=1)

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

       y: vector of responses.

       q: vector of quantiles.

       p: vector of probabilities

       n: number of values to generate

       m: vector of location parameters.

       s: vector of dispersion parameters.

       f: vector of skew parameters.

     log: if TRUE, log probabilities are supplied.

_A_u_t_h_o_r(_s):

     J.K. Lindsey

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

     'dexp' for the exponential distribution, 'dcauchy' for the Cauchy
     distribution, and 'dlaplace' for the Laplace distribution.

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

     dskewlaplace(5, 2, 1, 0.5)
     pskewlaplace(5, 2, 1, 0.5)
     qskewlaplace(0.95, 2, 1, 0.5)
     rskewlaplace(10, 2, 1, 0.5)

