Probability distribution looping

Question

I have this data set

DF:

Type        Value       Average     SD      Q.
S           AA+         3           1       30
S           AA          2           1       30
S           A           1           1       30
S           B          -2           1       30
S           BB -       -3           1       30
F           AA+         2       0.75        30
F           AA          1       0.75        30
F           A           0       0.75        30
F           B          -1       0.75        30
F           BB -       -2       0.75        30

I would like to make a probability distribution in loop by type and value like this

rnorm(n, mean = 0, sd = 1)  

rnorm(DF$Q., DF$Average, DF$SD)

I have list of unique values

    type_list <- unique(DF$Type)
    Value_list <- unique(DF$Value)


And now I am trying to loop it

  probability_distributions <- list()
    for (i in 1:length(type_list)) { 
      for (j in 1:length(Value_list) {
        
       pd <-  rnorm(DF$Q.[i,j], DF$Average[i,j], DF$SD[i,j])
         
       probability_distributions <- c(pd,    list(probability_distributions ))
      }
    }

I would like to get something like this

List:

    S AA+ 
1   -3.837712 
2   -3.690301 
3   -3.837331
4    -2.302341 ....

And have another 10 lists

Answer 1

You could do:

setNames(lapply(seq(nrow(DF)), function(i) {
  rnorm(DF$Q.[i], DF$Average[i], DF$SD[i])
}), paste(DF$Type, DF$Value))

#> $`S AA+`
#>  [1] 1.9993416 2.2418212 2.3885642 1.6832777 0.9925850 3.7680021 3.4057613 2.1682841
#>  [9] 3.9580758 4.8107193 0.4499855 4.1502551 4.2278937 3.1521032 2.4769162 1.8984066
#> [17] 2.1202697 2.3632997 0.8940686 2.3537416 3.9867934 2.2450999 4.5652049 2.9499507
#> [25] 3.1110287 3.4754710 2.0609961 2.2259544 2.5764415 4.7728795
#> 
#> $`S AA`
#>  [1]  2.42655066  1.90552983  0.88340457  1.91256485  2.39252609  1.63937783
#>  [7]  1.11201564  1.05358345  1.78008844  2.34222012  2.96992413  0.66454686
#> [13]  1.19912052 -0.04679634  2.11005622  2.71610037  2.25412060  3.22876219
#> [19]  2.58340401  1.41287523  3.44666536  2.44339404  2.57794689  1.07816504
#> [25]  1.75067329  0.77810135  1.92746035  3.36490125  1.54246898  2.06520022
#> 
#> $`S A`
#>  [1]  1.783980336 -0.587708073 -0.369364313  0.072480197  1.300841560  1.080468946
#>  [7]  2.246746831 -0.234449100  0.560930706 -1.101593953  2.618756171  2.084328491
#> [13]  0.359199093  0.747180174  0.865170727  2.795355992  1.038396717  1.412998289
#> [19]  1.699572123  1.689790945 -0.671059465  1.740048308  0.075875101  0.968311427
#> [25] -0.927792982  1.214303030 -0.005038866 -1.178953492 -0.672549131 -0.420722136
#> 
#> $`S B`
#>  [1] -1.44946836 -1.68956682 -1.31492609 -2.53191049 -1.81821454 -1.58840382
#>  [7] -2.08505905 -3.10670620 -0.87086640 -0.33198438  0.01910293 -1.10745196
#> [13] -2.18720468 -2.12769742 -2.30533014 -2.26286684 -2.05146864 -3.97266336
#> [19] -1.98877175 -1.76465514 -2.95036985 -3.75714798 -2.35996065 -5.12158956
#> [25] -0.32745289 -1.30945018 -2.97667032 -1.98486582 -2.16545418 -3.66021337
#> 
#> $`S BB-`
#>  [1] -3.878434 -2.034184 -4.155821 -3.751396 -3.745084 -1.772948 -3.190858 -2.445689
#>  [9] -2.228567 -3.380067 -4.128551 -2.829898 -3.358542 -1.557062 -3.519947 -3.310642
#> [17] -2.317263 -3.663578 -3.017951 -2.503409 -3.404275 -4.211649 -2.687256 -3.279862
#> [25] -5.019855 -2.730421 -2.868201 -4.678771 -3.525880 -3.175125
#> 
#> $`F AA+`
#>  [1] 1.5825269 2.4138863 0.8179614 1.2842804 1.6626024 3.0829298 1.8835594 1.2337108
#>  [9] 3.1538523 1.8266180 2.4139429 2.8413455 2.3071590 2.9751961 1.4068090 3.1989646
#> [17] 0.6328248 1.2684777 1.5601545 2.1748322 1.6449135 2.4373332 2.3150221 2.5091457
#> [25] 3.1118458 0.9310370 2.7274812 1.8009007 1.3976708 0.6672244
#> 
#> $`F AA`
#>  [1]  0.363222331  0.775391336 -0.455183359  0.729975409  1.382579640  0.026522186
#>  [7]  0.996364448 -0.008639176  0.961236861  1.671137345 -0.634911705  2.729812324
#> [13]  0.124187233  1.705322289  2.559326197  0.292131983  0.493409391  1.766237746
#> [19]  0.386872427  0.282159449  2.185839460  2.324832101  0.829723631  2.710832646
#> [25]  2.427810412  0.948533848  0.389605646  0.495058514  2.051522848  1.405012456
#> 
#> $`F A`
#>  [1]  0.481705627 -0.009539824  0.137159665 -0.366385935  0.851427552 -0.244538267
#>  [7]  1.493896900  0.440079671  0.741249918  1.106717951 -0.035215035 -1.325648324
#> [13] -0.457225479  0.444942684  0.902540415  0.156192620  0.629354519  0.707281075
#> [19]  0.771069839  0.560672883 -0.143570299  0.768517623 -0.378166481  0.261411645
#> [25] -0.382030406  0.358368343  0.375739047 -0.079185388  0.020481554  0.325286853
#> 
#> $`F B`
#>  [1] -1.84829836 -0.23448482 -0.79804428 -0.58858852 -1.12706587 -2.40883019
#>  [7] -0.43876960 -1.19507511 -0.53630451  0.53595272 -1.86671863  0.01470606
#> [13] -1.27564149 -1.04373285 -1.39916357 -1.37387536 -1.86260468 -0.90531931
#> [19] -0.64535208 -1.13989391 -2.21446484 -1.30206928 -0.69039082 -1.54053955
#> [25] -1.44254892 -1.87721996 -0.55640752 -1.50147921  1.37595324 -0.24022044
#> 
#> $`F BB-`
#>  [1] -2.1244905 -1.9981876 -2.5379765 -1.7889965 -1.9945386 -3.2972752 -3.3826052
#>  [8] -1.5490977 -3.7384532 -2.2852341 -0.7586263 -3.2471413 -1.7789528 -0.8225739
#> [15] -1.6160398 -1.0355732 -2.7256361 -1.5257080 -1.8626910 -0.9874129 -0.1345042
#> [22] -1.9140037 -1.1781947 -2.3020324 -2.2693023 -2.4145912 -3.0160062 -1.9449959
#> [29] -2.0292414 -1.4585976

Answer 2

Please always provide something we can copy-paste as a reproducible example. Here I created something for you.

library(dplyr)
library(data.table)
Type <- 1:3
Value <- 11:13
SD <- seq(0.1,0.3, by=0.1)
mean <- c(1,11,21)
df <- data.frame(Type, Value, SD, mean)
> df
  Type Value  SD mean
1    1    11 0.1    1
2    2    12 0.2   11
3    3    13 0.3   21

You want to create one rnorm series for all the possible combinations, that would be 9 values with my minimal example. expand.grid will do the heavy lifting.

> expand.grid(unique(types), unique(values)) %>% nrow
[1] 9

First you need to build your unique data.frame with the right means and SD's. Then you just call lapply to get a list containing your expected result.

# get unique combinations
unique.df <- expand.grid(types, values)
colnames(unique.df) <- c("Type", "Value")
# I suppose the mean and SD are determined by the type 
unique.df$mean <- df$mean[match(unique.df$Type, df$Type)]
unique.df$SD <- df$SD[match(unique.df$Type, df$Type)]
#convert to list by keeping names
unique.list <- setNames(split(unique.df, seq(nrow(unique.df))), rownames(unique.df))
probability_distributions <- lapply(unique.list, function(x) rnorm(x[["Value"]], x[["mean"]], x[["SD"]]))

Note that first here I create a dataframe which contains all the right information needed for your function.

> head(unique.df)
  Type Value probability_distributions mean  SD
1    1    11                 11.046879    1 0.1
2    2    11                  9.803352   11 0.2
3    3    11                 11.799637   21 0.3

Then I convert the unique.df data.frame into a list containing all its rows, by keeping the names, which is explained here

And finally, without any explicit loop, I can call lapply on this list. Most of the difficulty is to know how to arrange your data before building your results, so that you can avoid loops and use relatively elegant code such as lapply.

Full code:

library(dplyr)
Type <- 1:3
Value <- 11:13
SD <- seq(0.1,0.3, by=0.1)
mean <- c(1,11,21)
df <- data.frame(Type, Value, SD, mean)


# get unique combinations
unique.df <- expand.grid(types, values)
colnames(unique.df) <- c("Type", "Value")
# I suppose the mean and SD are determined by the type 
unique.df$mean <- df$mean[match(unique.df$Type, df$Type)]
unique.df$SD <- df$SD[match(unique.df$Type, df$Type)]
#convert to list by keeping names
unique.list <- setNames(split(unique.df, seq(nrow(unique.df))), rownames(unique.df))
probability_distributions <- lapply(unique.list, function(x) rnorm(x[["Value"]], x[["mean"]], x[["SD"]]))