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Summary of Conditional PMF

Source: R/04_pmf_conditional.R
summary_pmf_K_given_alpha.Rd

Returns a comprehensive summary of the conditional distribution \(K_J \mid \alpha\).

Usage

summary_pmf_K_given_alpha(J, alpha, logS)

Arguments

J

Integer; sample size.

alpha

Numeric; DP concentration parameter.

logS

Matrix; pre-computed log-Stirling matrix.

Value

A list with components:

J

Sample size

alpha

Concentration parameter

mean

Conditional mean \(E[K_J \mid \alpha]\)

var

Conditional variance \(Var(K_J \mid \alpha)\)

sd

Conditional standard deviation

mode

Most likely value of K

median

Median of K

quantiles

25th, 50th, and 75th percentiles

pmf

Full PMF vector

cdf

Full CDF vector

Examples

logS <- compute_log_stirling(50)
summary <- summary_pmf_K_given_alpha(50, 2.0, logS)
print(summary)
#> $J
#> [1] 50
#> 
#> $alpha
#> [1] 2
#> 
#> $mean
#> [1] 7.037626
#> 
#> $var
#> [1] 4.535558
#> 
#> $sd
#> [1] 2.129685
#> 
#> $mode
#> [1] 7
#> 
#> $median
#> [1] 7
#> 
#> $quantiles
#> q25 q50 q75 
#>   6   7   8 
#> 
#> $pmf
#>  [1] 0.000000e+00 7.843137e-04 7.026204e-03 2.892321e-02 7.366141e-02
#>  [6] 1.314732e-01 1.763027e-01 1.857343e-01 1.585811e-01 1.122778e-01
#> [11] 6.708833e-02 3.430261e-02 1.517696e-02 5.864045e-03 1.993746e-03
#> [16] 6.003097e-04 1.609381e-04 3.859325e-05 8.310542e-06 1.612342e-06
#> [21] 2.826321e-07 4.487020e-08 6.464443e-09 8.465460e-10 1.008981e-10
#> [26] 1.095623e-11 1.084651e-12 9.793755e-14 8.066710e-15 6.059886e-16
#> [31] 4.150099e-17 2.589106e-18 1.469829e-19 7.581980e-21 3.547300e-22
#> [36] 1.501824e-23 5.737591e-25 1.971294e-26 6.065905e-28 1.663393e-29
#> [41] 4.040285e-31 8.628062e-33 1.605042e-34 2.570824e-36 3.492630e-38
#> [46] 3.945285e-40 3.605028e-42 2.559734e-44 1.324882e-46 4.445912e-49
#> [51] 7.258631e-52
#> 
#> $cdf
#>  [1] 0.0000000000 0.0007843137 0.0078105182 0.0367337303 0.1103951411
#>  [6] 0.2418683565 0.4181710304 0.6039052892 0.7624864249 0.8747642097
#> [11] 0.9418525440 0.9761551529 0.9913321104 0.9971961556 0.9991899012
#> [16] 0.9997902109 0.9999511489 0.9999897422 0.9999980527 0.9999996651
#> [21] 0.9999999477 0.9999999926 0.9999999990 0.9999999999 1.0000000000
#> [26] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
#> [31] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
#> [36] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
#> [41] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
#> [46] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
#> [51] 1.0000000000
#>