# Cookbook part 3: Stats with and without out-of-stream variables¶

## Overview¶

One of Miller’s strengths is its compact notation: for example, given input of the form

``` head -n 5 ../data/medium
a=pan,b=pan,i=1,x=0.3467901443380824,y=0.7268028627434533
a=eks,b=pan,i=2,x=0.7586799647899636,y=0.5221511083334797
a=wye,b=wye,i=3,x=0.20460330576630303,y=0.33831852551664776
a=eks,b=wye,i=4,x=0.38139939387114097,y=0.13418874328430463
a=wye,b=pan,i=5,x=0.5732889198020006,y=0.8636244699032729
```

you can simply do

``` mlr --oxtab stats1 -a sum -f x ../data/medium
x_sum 4986.019682
```

or

``` mlr --opprint stats1 -a sum -f x -g b ../data/medium
b   x_sum
pan 965.763670
wye 1023.548470
zee 979.742016
eks 1016.772857
hat 1000.192668
```

rather than the more tedious

``` mlr --oxtab put -q '
@x_sum += \$x;
end {
emit @x_sum
}
' data/medium
x_sum 4986.019682
```

or

``` mlr --opprint put -q '
@x_sum[\$b] += \$x;
end {
emit @x_sum, "b"
}
' data/medium
b   x_sum
pan 965.763670
wye 1023.548470
zee 979.742016
eks 1016.772857
hat 1000.192668
```

The former (`mlr stats1` et al.) has the advantages of being easier to type, being less error-prone to type, and running faster.

Nonetheless, out-of-stream variables (which I whimsically call oosvars), begin/end blocks, and emit statements give you the ability to implement logic – if you wish to do so – which isn’t present in other Miller verbs. (If you find yourself often using the same out-of-stream-variable logic over and over, please file a request at https://github.com/johnkerl/miller/issues to get it implemented directly in C as a Miller verb of its own.)

The following examples compute some things using oosvars which are already computable using Miller verbs, by way of providing food for thought.

## Mean without/with oosvars¶

``` mlr --opprint stats1 -a mean -f x data/medium
x_mean
0.498602
```
``` mlr --opprint put -q '
@x_sum += \$x;
@x_count += 1;
end {
@x_mean = @x_sum / @x_count;
emit @x_mean
}
' data/medium
x_mean
0.498602
```

## Keyed mean without/with oosvars¶

``` mlr --opprint stats1 -a mean -f x -g a,b data/medium
a   b   x_mean
pan pan 0.513314
eks pan 0.485076
wye wye 0.491501
eks wye 0.483895
wye pan 0.499612
zee pan 0.519830
eks zee 0.495463
zee wye 0.514267
hat wye 0.493813
pan wye 0.502362
zee eks 0.488393
hat zee 0.509999
hat eks 0.485879
wye hat 0.497730
pan eks 0.503672
eks eks 0.522799
hat hat 0.479931
hat pan 0.464336
zee zee 0.512756
pan hat 0.492141
pan zee 0.496604
zee hat 0.467726
wye zee 0.505907
eks hat 0.500679
wye eks 0.530604
```
``` mlr --opprint put -q '
@x_sum[\$a][\$b] += \$x;
@x_count[\$a][\$b] += 1;
end{
for ((a, b), v in @x_sum) {
@x_mean[a][b] = @x_sum[a][b] / @x_count[a][b];
}
emit @x_mean, "a", "b"
}
' data/medium
a   b   x_mean
pan pan 0.513314
pan wye 0.502362
pan eks 0.503672
pan hat 0.492141
pan zee 0.496604
eks pan 0.485076
eks wye 0.483895
eks zee 0.495463
eks eks 0.522799
eks hat 0.500679
wye wye 0.491501
wye pan 0.499612
wye hat 0.497730
wye zee 0.505907
wye eks 0.530604
zee pan 0.519830
zee wye 0.514267
zee eks 0.488393
zee zee 0.512756
zee hat 0.467726
hat wye 0.493813
hat zee 0.509999
hat eks 0.485879
hat hat 0.479931
hat pan 0.464336
```

## Variance and standard deviation without/with oosvars¶

``` mlr --oxtab stats1 -a count,sum,mean,var,stddev -f x data/medium
x_count  10000
x_sum    4986.019682
x_mean   0.498602
x_var    0.084270
x_stddev 0.290293
```
``` cat variance.mlr
@n += 1;
@sumx += \$x;
@sumx2 += \$x**2;
end {
@mean = @sumx / @n;
@var = (@sumx2 - @mean * (2 * @sumx - @n * @mean)) / (@n - 1);
@stddev = sqrt(@var);
emitf @n, @sumx, @sumx2, @mean, @var, @stddev
}
```
``` mlr --oxtab put -q -f variance.mlr data/medium
n      10000
sumx   4986.019682
sumx2  3328.652400
mean   0.498602
var    0.084270
stddev 0.290293
```

You can also do this keyed, of course, imitating the keyed-mean example above.

## Min/max without/with oosvars¶

``` mlr --oxtab stats1 -a min,max -f x data/medium
x_min 0.000045
x_max 0.999953
```
``` mlr --oxtab put -q '@x_min = min(@x_min, \$x); @x_max = max(@x_max, \$x); end{emitf @x_min, @x_max}' data/medium
x_min 0.000045
x_max 0.999953
```

## Keyed min/max without/with oosvars¶

``` mlr --opprint stats1 -a min,max -f x -g a data/medium
a   x_min    x_max
pan 0.000204 0.999403
eks 0.000692 0.998811
wye 0.000187 0.999823
zee 0.000549 0.999490
hat 0.000045 0.999953
```
``` mlr --opprint --from data/medium put -q '
@min[\$a] = min(@min[\$a], \$x);
@max[\$a] = max(@max[\$a], \$x);
end{
emit (@min, @max), "a";
}
'
a   min      max
pan 0.000204 0.999403
eks 0.000692 0.998811
wye 0.000187 0.999823
zee 0.000549 0.999490
hat 0.000045 0.999953
```

## Delta without/with oosvars¶

``` mlr --opprint step -a delta -f x data/small
a   b   i x                   y                   x_delta
pan pan 1 0.3467901443380824  0.7268028627434533  0
eks pan 2 0.7586799647899636  0.5221511083334797  0.411890
wye wye 3 0.20460330576630303 0.33831852551664776 -0.554077
eks wye 4 0.38139939387114097 0.13418874328430463 0.176796
wye pan 5 0.5732889198020006  0.8636244699032729  0.191890
```
``` mlr --opprint put '\$x_delta = is_present(@last) ? \$x - @last : 0; @last = \$x' data/small
a   b   i x                   y                   x_delta
pan pan 1 0.3467901443380824  0.7268028627434533  0
eks pan 2 0.7586799647899636  0.5221511083334797  0.411890
wye wye 3 0.20460330576630303 0.33831852551664776 -0.554077
eks wye 4 0.38139939387114097 0.13418874328430463 0.176796
wye pan 5 0.5732889198020006  0.8636244699032729  0.191890
```

## Keyed delta without/with oosvars¶

``` mlr --opprint step -a delta -f x -g a data/small
a   b   i x                   y                   x_delta
pan pan 1 0.3467901443380824  0.7268028627434533  0
eks pan 2 0.7586799647899636  0.5221511083334797  0
wye wye 3 0.20460330576630303 0.33831852551664776 0
eks wye 4 0.38139939387114097 0.13418874328430463 -0.377281
wye pan 5 0.5732889198020006  0.8636244699032729  0.368686
```
``` mlr --opprint put '\$x_delta = is_present(@last[\$a]) ? \$x - @last[\$a] : 0; @last[\$a]=\$x' data/small
a   b   i x                   y                   x_delta
pan pan 1 0.3467901443380824  0.7268028627434533  0
eks pan 2 0.7586799647899636  0.5221511083334797  0
wye wye 3 0.20460330576630303 0.33831852551664776 0
eks wye 4 0.38139939387114097 0.13418874328430463 -0.377281
wye pan 5 0.5732889198020006  0.8636244699032729  0.368686
```

## Exponentially weighted moving averages without/with oosvars¶

``` mlr --opprint step -a ewma -d 0.1 -f x data/small
a   b   i x                   y                   x_ewma_0.1
pan pan 1 0.3467901443380824  0.7268028627434533  0.346790
eks pan 2 0.7586799647899636  0.5221511083334797  0.387979
wye wye 3 0.20460330576630303 0.33831852551664776 0.369642
eks wye 4 0.38139939387114097 0.13418874328430463 0.370817
wye pan 5 0.5732889198020006  0.8636244699032729  0.391064
```
``` mlr --opprint put '
begin{ @a=0.1 };
\$e = NR==1 ? \$x : @a * \$x + (1 - @a) * @e;
@e=\$e
' data/small
a   b   i x                   y                   e
pan pan 1 0.3467901443380824  0.7268028627434533  0.346790
eks pan 2 0.7586799647899636  0.5221511083334797  0.387979
wye wye 3 0.20460330576630303 0.33831852551664776 0.369642
eks wye 4 0.38139939387114097 0.13418874328430463 0.370817
wye pan 5 0.5732889198020006  0.8636244699032729  0.391064
```