Hotelling-type \(T^2\) statistic for one cumulant set

Computes the log-cumulant \(T^2\) goodness-of-fit statistic for a single choice of cumulant orders V, with the asymptotic chi-squared reference using the corrected (full-rank) degrees of freedom.

Usage

T2_one(x, dist, V, fit = NULL)

Arguments

x

Numeric vector of positive observations.

dist

Character; null distribution name.

V

Integer vector of cumulant orders (e.g. c(2,3)).

fit

Optional precomputed mle_fit object.

Value

A list with the statistic T2, degrees of freedom df, and asymptotic p-value p_asym.

Examples

set.seed(1); x <- rdist(100, "Weibull", c(2, 1))
T2_one(x, "Weibull", V = c(2, 3))
#> $T2
#> [1] 1.959033
#> 
#> $df
#> [1] 1
#> 
#> $p_chisq
#> [1] 0.1616167
#> 
#> $p_F
#> [1] 0.1647425
#> 
#> $theta
#> [1] 2.2534731 0.9586402
#> 
#> $d
#> [1] -0.03627176  0.08444942
#> 
#> $Kd
#>             [,1]        [,2]
#> [1,]  0.02121533 -0.09598141
#> [2,] -0.09598141  0.39585293
#> 
#> $eigmin
#> [1] -0.001943338
#> 
#> $conv
#> [1] TRUE
#>