 NCL Home > Documentation > Functions > General applied math, Statistics

dim_stat4_n

Computes the first four moments (average, sample variance, skewness, and kurtosis) of the given dimension(s) for all other dimensions. Available in version 5.1.1 and later.

Prototype

```	function dim_stat4_n (
x        : numeric,
dims [*] : integer
)

return_val  :  float or double
```

Arguments

x

A variable of numeric type and any dimensionality.

dims

The dimension(s) of x on which to calculate the first four moments. Must be consecutive and monotonically increasing.

Return value

The output will be double if x is double, and float otherwise.

The output dimensionality will be 4 x all-but-the-dims' dimensions of the input. The average is at (0,"dims"), variance (1,"dims"), skewness (2,"dims") and kurtosis (3,"dims"). (See examples below.)

Description

The dim_stat4_n function computes the first four moments (average, sample variance, skewness, and kurtosis) of all elements of the dimensions indicated by dims for each index of the remaining dimensions Missing values are ignored.

The skewness (third moment) is a measure departure from symmetry. If skew>0 [skew<0], the distribution trails off to the right [left].

The coefficient of kurtosis (fourth moment) measures normality. The normal distribution has a kurtosis of 3. This value is subtracted from the calculated kurtosis. Thus, negative values are possible and the returned value is kurtosis relative to the normal distribution. If kurtosis > 0 [<0], it is usually more sharply peaked [flatter] than the normal distribution (leptokurtic and platykurtic, respectively). E.g., a rectangular function has a kurtosis of -1.2 (=1.8-3) relative to the normal distribution.

The dim_num_n function can be used to determine the number of missing values. Eg:

Nx = dim_num_n(ismissing(x,0))

Examples

Example 1: Let x be a 1-dimensional array. Then:

```  xstat = dim_stat4_n(x,0)
```
will yield a one-dimensional array of length 4. xstat(0) contains the mean; xstat(1) = variance; xstat(2) = skewness; xstat(3) = kurtosis.

Note: when operating across the rightmost dimension, it is simpler to use dim_stat4.

Example 2

Let z be of size (ntim,nlat,mlon). Then, for each time and latitude, the the first four moments of each longitude (rightmost dimension) can be determined via:

```    zLon = dim_stat4_n( z, 2 )    ; ==> zLon(4,ntim,nlat)
```
Example 3: Let x be a 4-dimensional array with named dimensions (time, lev, lat, lon) and dimension sizes (ntim, klev, nlat, mlon). To determine the four moments in time:

```  xstat = dim_stat4_n(x,0)   ; ==> (4,klev,nlat,mlon)
```
Example 4: Let x be as in example 3. To determine the four moments in time and level:

```  xstat = dim_stat4_n(x,(/0,1/))   ; ==> (4,nlat,mlon)
```