Fit Empirical Distribution

Fit Empirical Distribution

fit_empirical(x)

Arguments

x

integer or double vector

Value

if integer vector then list of family functions for d, p, q, r, and parameters based on each integer value. if it is a double vector then list of family functions for d, p, q, r, and parameters based on Freedman-Diaconis rule for optimal number of histogram bins.

Examples

set.seed(562)
x <- rpois(100, 5)
empDis <- fit_empirical(x)

# probability density function
plot(empDis$dempDis(0:10),
     xlab = 'x',
     ylab = 'dempDis')

# cumulative distribution function
plot(x = 0:10,
     y = empDis$pempDis(0:10),
     #type = 'l',
     xlab = 'x',
     ylab = 'pempDis')

# quantile function
plot(x = seq(.1, 1, .1),
     y = empDis$qempDis(seq(.1, 1, .1)),
     type = 'p',
     xlab = 'x',
     ylab = 'qempDis')

# random sample from fitted distribution
summary(empDis$r(100))
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>    1.00    3.00    5.00    4.71    7.00   10.00 

empDis$parameters
#>    0    1    2    3    4    5    6    7    8    9   10 
#> 0.01 0.08 0.14 0.09 0.08 0.24 0.07 0.11 0.07 0.09 0.02 

set.seed(562)
x <- rexp(100, 1/5)
empCont <- fit_empirical(x)

# probability density function
plot(x = 0:10,
     y = empCont$dempCont(0:10),
     xlab = 'x',
     ylab = 'dempCont')

# cumulative distribution function
plot(x = 0:10,
     y = empCont$pempCont(0:10),
     #type = 'l',
     xlab = 'x',
     ylab = 'pempCont')

# quantile function
plot(x = seq(.5, 1, .1),
     y = empCont$qempCont(seq(.5, 1, .1)),
     type = 'p',
     xlab = 'x',
     ylab = 'qempCont')

# random sample from fitted distribution
summary(empCont$r(100))
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   1.394   1.394   4.205   4.871   4.205  32.200 

empCont$parameters
#> (-0.0217,2.81]     (2.81,5.6]      (5.6,8.4]     (8.4,11.2]      (11.2,14] 
#>           0.42           0.27           0.12           0.05           0.06 
#>      (14,16.8]    (16.8,19.6]    (19.6,22.4]    (22.4,25.2]      (25.2,28] 
#>           0.01           0.04           0.01           0.01           0.00 
#>      (28,30.8]    (30.8,33.6] 
#>           0.00           0.01