Summary Statistics for w₁ Distribution

Computes comprehensive summary statistics for the w₁ distribution.

Usage

summary_w1(
  a,
  b,
  probs = c(0.05, 0.25, 0.5, 0.75, 0.95),
  M = .QUAD_NODES_DEFAULT
)

Arguments

a

Numeric; shape parameter of the Gamma prior on α (a > 0).

b

Numeric; rate parameter of the Gamma prior on α (b > 0).

probs

Numeric vector; quantile probabilities. Default is c(0.05, 0.25, 0.5, 0.75, 0.95).

M

Integer; number of quadrature nodes for mean/variance. Default is 80.

Value

A list of class "w1_summary" containing:

mean

E(w₁)

var

Var(w₁)

sd

SD(w₁) = sqrt(Var(w₁))

median

Median of w₁

quantiles

Named vector of quantiles

prob_gt_50

P(w₁ > 0.5), dominance indicator

prob_gt_90

P(w₁ > 0.9), extreme dominance indicator

params

List of input parameters (a, b)

See also

cdf_w1, quantile_w1, mean_w1

Examples

# Standard summary
summary_w1(a = 2, b = 1)
#> w1 Distribution Summary
#> ============================================= 
#> 
#> Gamma prior: alpha ~ Gamma(2.0000, 1.0000)
#> E[alpha] = 2.0000, CV(alpha) = 70.71%
#> 
#> Location and Scale:
#> ------------------------------ 
#>   Mean:   0.4037
#>   Median: 0.3391
#>   SD:     0.2995
#> 
#> Quantiles:
#> ------------------------------ 
#>   q5: 0.0256
#>   q25: 0.1433
#>   q50: 0.3391
#>   q75: 0.6321
#>   q95: 0.9689 
#> 
#> Dominance Risk:
#> ------------------------------ 
#>   P(w1 > 0.5): 0.3488
#>   P(w1 > 0.9): 0.0917

# Lee et al. DP-inform prior
summary_w1(a = 1.6, b = 1.22)
#> w1 Distribution Summary
#> ============================================= 
#> 
#> Gamma prior: alpha ~ Gamma(1.6000, 1.2200)
#> E[alpha] = 1.3115, CV(alpha) = 79.06%
#> 
#> Location and Scale:
#> ------------------------------ 
#>   Mean:   0.5084
#>   Median: 0.4839
#>   SD:     0.3244
#> 
#> Quantiles:
#> ------------------------------ 
#>   q5: 0.0390
#>   q25: 0.2136
#>   q50: 0.4839
#>   q75: 0.8139
#>   q95: 0.9988 
#> 
#> Dominance Risk:
#> ------------------------------ 
#>   P(w1 > 0.5): 0.4868
#>   P(w1 > 0.9): 0.1833