# cumpercentile

Syntax

cumpercentile(X, percent, [interpolation=’linear’])

Please see Cumulative Window Functions (cum-functions) for the parameters and windowing logic.

Arguments

X is a vector.

percent is an integer or a floating number between 0 and 100.

interpolation is a string indicating the interpolation method to use if the specified percentile is between two elements in X (assuming the i-th and (i+1)-th element in the sorted X) . It can take the following values:

• ‘linear’: Return X(i)+(X(t+1)-X(t))*fraction, where fraction = ((percentile100)-(i(size-1)))(1(size-1))

• ‘lower’: Return X(i)

• ‘higher’: Return X(i+1)

• ‘nearest’: Return X(i) or X(i+1) that is closest to the specified percentile

• ‘midpoint’: Return (X(i)+X(i+1))2

The default value of interpolation is ‘linear’.

Details

If X is a vector, cumulatively calculate the given percentile of a vector. The calculation ignores NULL values.

If X is a matrix, conduct the aforementioned calculation within each column of X. The result is a matrix with the same shape as X.

Examples

```\$ a=1..10;

\$ cumpercentile(a,25);
[1,1.25,1.5,1.75,2,2.25,2.5,2.75,3,3.25]

\$ cumpercentile(a,25,'lower');
[1,1,1,1,2,2,2,2,3,3]

\$ cumpercentile(a,25,'higher');
[1,2,2,2,2,3,3,3,3,4]

\$ cumpercentile(a,25,'midpoint');
[1,1.5,1.5,1.5,2,2.5,2.5,2.5,3,3.5]

\$ cumpercentile(a,25,'nearest');
[1,1,1,2,2,2,2,3,3,3]

\$ cumpercentile(a,50.5);
[1,1.505,2.01,2.515,3.02,3.525,4.03,4.535,5.04,5.545]

\$ m=matrix(1..10, 11..20);
\$ m;
```

#0

#1

1

11

2

12

3

13

4

14

5

15

6

16

7

17

8

18

9

19

10

20

```\$ cumpercentile(m,25);
```

#0

#1

1

11

1.25

11.25

1.5

11.5

1.75

11.75

2

12

2.25

12.25

2.5

12.5

2.75

12.75

3

13

3.25

13.25

Related functions: percentile