# [R] mixture univariate distributions fit

PIKAL Petr petr@p|k@| @end|ng |rom prechez@@cz
Wed Dec 29 12:05:22 CET 2021

```Dear all

I have data which are either density distribution estimate or cummulative
density distribution estimate (temp1, temp2 below). I would like to get
values (mu, sd) for underlaying original data but they are not available.

I found mixtools package which calculate what I need but it requires
original data (AFAIK). They could be generated from e.g. temp1 by

set.seed(111)
x<- sample(temp1\$velik, size=100000, replace=TRUE, prob=temp1\$proc)

library(mixtools)
fit <- normalmixEM(x)
plot(fit, which=2)
summary(fit)
summary of normalmixEM object:
comp 1     comp 2
lambda   0.576346   0.423654
mu     170.784520 229.192823
sigma    7.203491  10.793461
loglik at estimate:  -424062.7
>

Is there any way how to get such values directly from density or cummulative
density estimation without generating fake data by sample?

Best regards
Petr

temp1 <- structure(list(velik = c(155, 156.8, 157.9, 158.8, 159.6, 160.4,
161.2, 161.9, 162.5, 163.1, 163.8, 164.3, 164.7, 165.3, 165.8,
166.2, 166.7, 167.2, 167.7, 168.2, 168.7, 169.1, 169.6, 170.1,
170.6, 171.1, 171.6, 172, 172.5, 173, 173.5, 174, 174.5, 175.1,
175.7, 176.3, 177, 177.6, 178.3, 179.1, 179.9, 180.6, 181.4,
182.4, 183.5, 184.7, 186.1, 187.9, 189.8, 192, 194.4, 197, 200.1,
203.5, 206.7, 209.2, 211.3, 213.1, 214.8, 216.3, 217.4, 218.5,
219.5, 220.4, 221.3, 222.1, 223, 223.7, 224.5, 225.2, 225.9,
226.7, 227.5, 228.2, 228.9, 229.6, 230.4, 231.2, 231.9, 232.6,
233.4, 234.2, 235, 235.9, 236.8, 237.7, 238.6, 239.7, 241, 242.3,
243.6, 245.2, 247.1, 249.3, 251.9, 255.3, 260, 266, 274.9, 323.4
), proc = c(0.6171, 1.583, 1.371, 2.13, 1.828, 2.095, 1.994,
2.694, 2.824, 2.41, 2.909, 3.768, 3.179, 3.029, 3.798, 3.743,
3.276, 3.213, 3.579, 2.928, 4.634, 3.415, 3.473, 3.135, 3.476,
3.759, 3.726, 3.9, 3.593, 2.89, 3.707, 4.08, 2.846, 2.685, 3.394,
2.737, 2.693, 2.878, 2.248, 2.368, 2.258, 2.662, 1.866, 1.895,
1.457, 1.513, 1.181, 1.008, 0.9641, 0.799, 0.7878, 0.7209, 0.5869,
0.5778, 0.7313, 0.9531, 1.053, 1.317, 1.247, 1.739, 2.064, 1.99,
2.522, 2.401, 2.48, 2.687, 2.797, 2.918, 3.243, 3.055, 3.009,
2.89, 3.037, 3.25, 3.349, 3.141, 2.771, 2.985, 3.203, 3.298,
3.215, 2.637, 2.683, 2.782, 2.632, 2.625, 2.475, 2.014, 1.781,
1.987, 1.627, 1.374, 1.352, 0.9441, 1.01, 0.5737, 0.5265, 0.3794,
0.2513, 0.0351)), row.names = 2:101, class = "data.frame")

temp2 <- structure(list(velik = c(153.8, 156.3, 157.3, 158.4, 159.2, 160.1,
160.8, 161.6, 162.2, 162.8, 163.5, 164, 164.5, 165, 165.5, 166,
166.4, 166.9, 167.5, 167.9, 168.5, 168.9, 169.4, 169.8, 170.4,
170.9, 171.3, 171.8, 172.2, 172.7, 173.3, 173.8, 174.2, 174.8,
175.5, 176, 176.6, 177.3, 177.9, 178.7, 179.5, 180.3, 180.9,
181.9, 182.9, 184.1, 185.3, 186.9, 188.8, 190.8, 193.2, 195.6,
198.4, 201.8, 205.3, 208.1, 210.3, 212.3, 213.9, 215.7, 216.9,
218, 219.1, 219.9, 220.8, 221.7, 222.6, 223.4, 224.1, 224.8,
225.6, 226.3, 227.1, 227.8, 228.5, 229.2, 230, 230.8, 231.6,
232.3, 233, 233.7, 234.6, 235.5, 236.3, 237.2, 238.1, 239.1,
240.3, 241.6, 242.9, 244.4, 246.1, 248, 250.6, 253.1, 257.6,
262.5, 269.5, 280.4, 372.9), proc = c(0, 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55,
56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100)), row.names = c(NA,
101L), class = "data.frame")
>

>
```