Mapper for marginal distribution transformation

Constructs a mapper that transforms the marginal distribution state from \(\textrm{N}(0,1)\) to the distribution of a given (continuous) quantile function. The ... arguments are used as parameter arguments to qfun, pfun, dfun, and dqfun.

Usage

bm_marginal(qfun, pfun = NULL, dfun = NULL, dqfun = NULL, ..., inverse = FALSE)

bru_mapper_marginal(...)

Arguments

qfun

A quantile function, supporting lower.tail and log.p arguments, like stats::qnorm().

pfun

A CDF, supporting lower.tail and log.p arguments, like stats::pnorm(). Only needed and used when xor(mapper[["inverse"]], reverse) is TRUE in a method call. Default NULL

dfun

A pdf, supporting log argument, like stats::dnorm(). If NULL (default), uses finite differences on qfun or pfun instead.

dqfun

A function evaluating the reciprocal of the derivative of qfun. If NULL (default), uses dfun(qfun(...),...) or finite differences on qfun or pfun instead.

...

Arguments passed on to bm_marginal()

inverse

logical; If FALSE (default), bm_marginal() defines a mapping from standard Normal to a specified distribution. If TRUE, it defines a mapping from the specified distribution to a standard Normal.

See also

bru_mapper, bru_mapper_generics

Other mappers: bm_aggregate(), bm_collect(), bm_const(), bm_factor(), bm_fm_mesh_1d, bm_fmesher(), bm_harmonics(), bm_index(), bm_linear(), bm_logsumexp(), bm_matrix(), bm_mesh_B(), bm_multi(), bm_pipe(), bm_repeat(), bm_scale(), bm_shift(), bm_sum(), bm_taylor(), bru_get_mapper(), bru_mapper()

Other specific bm_marginal method implementations: ibm_eval(), ibm_jacobian(), ibm_n(), ibm_n_output(), ibm_values()

Examples

m <- bm_marginal(qexp, pexp, rate = 1 / 8)
(val <- ibm_eval(m, state = -5:5))
#>  [1] 2.293213e-06 2.533739e-04 1.080648e-02 1.841033e-01 1.382030e+00
#>  [6] 5.545177e+00 1.472817e+01 3.026547e+01 5.286181e+01 8.288081e+01
#> [11] 1.205200e+02
ibm_eval(m, state = val, reverse = TRUE)
#>  [1] -5 -4 -3 -2 -1  0  1  2  3  4  5
m <- bm_marginal(qexp, pexp, dexp, rate = 1 / 8)
ibm_eval2(m, state = -3:3)
#> $offset
#> [1]  0.01080648  0.18410327  1.38203023  5.54517744 14.72817316 30.26547467
#> [7] 52.86180977
#> 
#> $jacobian
#> 7 x 7 diagonal matrix of class "ddiMatrix"
#>      [,1]       [,2]      [,3]   [,4]     [,5]     [,6]     [,7]    
#> [1,] 0.03550271         .      .        .        .        .        .
#> [2,]          . 0.4419829      .        .        .        .        .
#> [3,]          .         . 2.3008        .        .        .        .
#> [4,]          .         .      . 6.383076        .        .        .
#> [5,]          .         .      .        . 12.20108        .        .
#> [6,]          .         .      .        .        . 18.98572        .
#> [7,]          .         .      .        .        .        . 26.26479
#>