はじめに

手持ちの単変量の分布を確率密度関数に当てはめて母数を推定する（よくわからない）

使うデータは他のページで作成したdf.testDATA

スクリプト

library(fitdistrplus)
# 分布のテスト
x <- df.testDATA$Time2Onset
y <- max(df.testDATA$Time2Onset)
min(df.testDATA$Time2Onset)
################ distribution test ################ 

normmlefit <- fitdist(x, "norm", "mle"); fit <- normmlefit; gofstat(fit); plot(fit)
lnormmlefit <- fitdist(x + 0.1, "lnorm", "mle"); fit <- lnormmlefit; gofstat(fit); plot(fit)
poismlefit <- fitdist(x, "pois", "mle"); fit <- poismlefit; gofstat(fit); plot(fit)
expmlefit <- fitdist(x, "exp", "mle"); fit <- expmlefit; gofstat(fit); plot(fit)
gammammefit <- fitdist(x, "gamma", "mme"); fit <- gammamlefit; gofstat(fit); plot(fit)
nbinommlefit <- fitdist(x, "nbinom", "mle"); fit <- nbinommlefit; gofstat(fit); plot(fit)
geommlefit <- fitdist(x, "geom", "mle"); fit <- geommlefit; gofstat(fit); plot(fit)
betammefit <- fitdist(x/y, "beta", "mme"); fit <- betamlefit; gofstat(fit); plot(fit)
unifmlefit <- fitdist(x, "unif", "mle"); fit <- unifmlefit; gofstat(fit); plot(fit)
logismlefit <- fitdist(x, "logis", "mle"); fit <- logismlefit; gofstat(fit); plot(fit)

結果

よくフィットしてそうなのはbetaかgammaの様です

ロジスティック分布

Fitting of the distribution ' logis ' by maximum likelihood 
Parameters : 
         estimate Std. Error
location 58.31789   2.418478
scale    45.17608   1.249104
Loglikelihood:  -5863.559   AIC:  11731.12   BIC:  11740.93 
Correlation matrix:
          location     scale
location 1.0000000 0.1570439
scale    0.1570439 1.0000000

一様の分布（定数）

Fitting of the distribution ' unif ' by maximum likelihood 
Parameters : 
    estimate Std. Error
min        0         NA
max      682         NA
Loglikelihood:  -6525.03   AIC:  13054.06   BIC:  13063.87 
Correlation matrix:
[1] NA

beta分布

Fitting of the distribution ' beta ' by matching moments 
Parameters : 
        estimate
shape1 0.4604008
shape2 3.6574364
Loglikelihood:  NaN   AIC:  NaN   BIC:  NaN

geom分布

Fitting of the distribution ' geom ' by maximum likelihood 
Parameters : 
       estimate   Std. Error
prob 0.01294465 0.0004042749
Loglikelihood:  -5340.572   AIC:  10683.14   BIC:  10688.05

 

負の二項分布

Fitting of the distribution ' nbinom ' by maximum likelihood 
Parameters : 
       estimate Std. Error
size  0.7293184 0.02936535
mu   76.2394754 2.83607459
Loglikelihood:  -5307.489   AIC:  10618.98   BIC:  10628.79 
Correlation matrix:
             size           mu
size 1.0000000000 0.0001760878
mu   0.0001760878 1.0000000000

 

gamma分布

Fitting of the distribution ' gamma ' by matching moments 
Parameters : 
         estimate
shape 0.644237078
rate  0.008448789
Loglikelihood:  Inf   AIC:  -Inf   BIC:  -Inf

 

指数分布

Fitting of the distribution ' exp ' by maximum likelihood 
Parameters : 
       estimate   Std. Error
rate 0.01311441 0.0004122862
Loglikelihood:  -5334.044   AIC:  10670.09   BIC:  10675

 

ポワソン分布

Fitting of the distribution ' pois ' by maximum likelihood 
Parameters : 
       estimate Std. Error
lambda   76.252  0.2761377
Loglikelihood:  -48448.44   AIC:  96898.87   BIC:  96903.78

 

対数正規分布

Fitting of the distribution ' lnorm ' by maximum likelihood 
Parameters : 
        estimate Std. Error
meanlog 3.477753 0.05160282
sdlog   1.631824 0.03648864
Loglikelihood:  -5386.39   AIC:  10776.78   BIC:  10786.6 
Correlation matrix:
        meanlog sdlog
meanlog       1     0
sdlog         0     1

 

 

正規分布

Fitting of the distribution ' norm ' by maximum likelihood 
Parameters : 
     estimate Std. Error
mean 76.25200   3.004195
sd   95.00104   2.124288
Loglikelihood:  -5972.826   AIC:  11949.65   BIC:  11959.47 
Correlation matrix:
     mean sd
mean    1  0
sd      0  1