Exponential              package:stats              R Documentation

_T_h_e _E_x_p_o_n_e_n_t_i_a_l _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Density, distribution function, quantile function and random
     generation for the exponential distribution with rate 'rate'
     (i.e., mean '1/rate').

_U_s_a_g_e:

     dexp(x, rate = 1, log = FALSE)
     pexp(q, rate = 1, lower.tail = TRUE, log.p = FALSE)
     qexp(p, rate = 1, lower.tail = TRUE, log.p = FALSE)
     rexp(n, rate = 1)

_A_r_g_u_m_e_n_t_s:

    x, q: vector of quantiles.

       p: vector of probabilities.

       n: number of observations. If 'length(n) > 1', the length is
          taken to be the number required.

    rate: vector of rates.

log, log.p: logical; if TRUE, probabilities p are given as log(p).

lower.tail: logical; if TRUE (default), probabilities are P[X <= x],
          otherwise, P[X > x].

_D_e_t_a_i_l_s:

     If 'rate' is not specified, it assumes the default value of '1'.

     The exponential distribution with rate lambda has density

                     f(x) = lambda e^(- lambda x)

     for x >= 0.

_V_a_l_u_e:

     'dexp' gives the density, 'pexp' gives the distribution function,
     'qexp' gives the quantile function, and 'rexp' generates random
     deviates.

_N_o_t_e:

     The cumulative hazard H(t) = - log(1 - F(t)) is '-pexp(t, r, lower
     = FALSE, log = TRUE)'.

_S_o_u_r_c_e:

     'dexp', 'pexp' and 'qexp' are all calculated from numerically
     stable versions of the definitions.

     'rexp' uses

     Ahrens, J. H. and Dieter, U. (1972). Computer methods for sampling
     from the exponential and normal distributions. _Communications of
     the ACM_, *15*, 873-882.

_R_e_f_e_r_e_n_c_e_s:

     Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) _The New S
     Language_. Wadsworth & Brooks/Cole.

     Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) _Continuous
     Univariate Distributions_, volume 1, chapter 19. Wiley, New York.

_S_e_e _A_l_s_o:

     'exp' for the exponential function, 'dgamma' for the gamma
     distribution and 'dweibull' for the Weibull distribution, both of
     which generalize the exponential.

_E_x_a_m_p_l_e_s:

     dexp(1) - exp(-1) #-> 0

