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

# pdfxy

Generates a joint probability density distribution. (Please use pdfxy_conform.)

## Prototype

```load "\$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"  ; This library is automatically loaded
; from NCL V6.2.0 onward.
; No need for user to explicitly load.

function pdfxy (
x         : numeric,
y         : numeric,
nbinx [1] : integer,
nbiny [1] : integer,
opt   [1] : logical
)

return_val [*] :  double
```

## Arguments

x

An array of any dimensionality.

y

An array of the same dimensionality of x. The pdfxy_conform function can be used if y is of different dimensionality.

nbinx

Number of bins to use for x. Specifying 0 will result in 25 bins being used. Otherwise, this must be greater than 2.

nbiny

Number of bins to use for y. Specifying 0 will result in 25 bins being used. Otherwise, this must be greater than 2. This may be different than nbinx

opt

Attributes may be associated with this variable. The attributes will alter the default behavior of the pdfxy function.

Setting opt=True will activate use of the options.

• binx_min - minimum value for the x bin boundary.
• biny_min - minimum value for the y bin boundary.
• binx_max - maximum value for the x bin boundary.
• biny_max - maximum value for the y bin boundary.
• binx_nice - let NCL calculate "nice" bin boundary values for x
• biny_nice - let NCL calculate "nice" bin boundary values for y

## Return value

A two-dimensional array of size (nbiny,nbinx). Values will be in percent of total. Numerous attributes will be associated with the return variable. These will include:

• nbinx - the number of bins used for x.
• nbiny - the number of bins used for y.
• binx_spacing - the spacing of the bins used for x.
• biny_spacing - the spacing of the bins used for y.
• binx_bound_min - the minimum boundary bin value for x.
• biny_bound_min - the minimum boundary bin value for y.
• binx_bound_max - the maximum boundary bin value for x.
• biny_bound_max - the maximum boundary bin value for y.
• binx_center - a one-dimensional array of size nbinx containing the center points of each bin. For plotting these can be used as the "x" [abscissa].
• biny_center - a one-dimensional array of size nbiny containing the center points of each bin. For plotting these can be used as the "y" [ordinate].
• binx_bounds - a one-dimensional array of size (nbinx +1) containing the boundaries of each bin.
• biny_bounds - a one-dimensional array of size (nbiny +1) containing the boundaries of each bin.

## Description

A bug was fixed in NCL version 6.2.0 in which values exactly equal to the rightmost edge of the rightmost bin were not getting counted correctly. PLEASE use the pdfxy_conform interface to pdfxy. The argument sequence is the same.

The input arrays x and y are partitioned into nbinx and y sections. The user may set the desired minimum, maximum and the number of bins. The returned PDF will be in percent of total.

## Examples

Example 1

Using default settings:

```  x    = random_normal ( 0,50, (/96,144/))
y    = random_normal (10,25, dimsizes(x))
pdf2 = pdfxy(x, y, 0, 0, False)   ; default is 25 bins
printVarSummary( pdf2 )
print("pdf2@binx_center="+pdf2@binx_center +"   " \
+"pdf2@biny_center="+pdf2@biny_center)
```
The (edited) printVarSummary yields:
```
Variable: pdf2
Type: double
Total Size: 5000 bytes
625 values
Number of Dimensions: 2
Dimensions and sizes:   [y | 25] x [x | 25]
Coordinates:
y: [-49.46327590942383..133.8606376647949]
x: [-194.5512237548828..204.6318817138672]
Number Of Attributes: 26
_FillValue :  1e+20
[snip]
xMIN :        -202.8675384521484
xMAX :        212.9481964111328
binx_center :
binx_bounds :
binx_bound_min :      -202.8675384521484
binx_bound_max :      212.9481964111328
binx_spacing :        16.63262939453125
nbinsx :      25
yMIN :        -53.28252410888672
yMAX :        137.6798858642578
biny_center :
biny_bounds :
biny_bound_min :      -53.28252410888672
biny_bound_max :      137.6798858642578
biny_spacing :        7.638496398925781
nbinsy :      25
[snip]

```
The print("pdf2@binx_center="+pdf2@binx_center+" pdf2@biny_center="+pdf2@biny_center) yields:
```
(0)     pdf2@binx_center=-194.551   pdf2@biny_center=-49.4633
(1)     pdf2@binx_center=-177.919   pdf2@biny_center=-41.8248
(2)     pdf2@binx_center=-161.286   pdf2@biny_center=-34.1863
(3)     pdf2@binx_center=-144.653   pdf2@biny_center=-26.5478
(4)     pdf2@binx_center=-128.021   pdf2@biny_center=-18.9093
(5)     pdf2@binx_center=-111.388   pdf2@biny_center=-11.2708
(6)     pdf2@binx_center=-94.7554   pdf2@biny_center=-3.6323
(7)     pdf2@binx_center=-78.1228   pdf2@biny_center=4.0062
(8)     pdf2@binx_center=-61.4902   pdf2@biny_center=11.6447
(9)     pdf2@binx_center=-44.8576   pdf2@biny_center=19.2832
(10)    pdf2@binx_center=-28.2249   pdf2@biny_center=26.9217
(11)    pdf2@binx_center=-11.5923   pdf2@biny_center=34.5602
(12)    pdf2@binx_center=5.04033    pdf2@biny_center=42.1987
(13)    pdf2@binx_center=21.673     pdf2@biny_center=49.8372
(14)    pdf2@binx_center=38.3056    pdf2@biny_center=57.4757
(15)    pdf2@binx_center=54.9382    pdf2@biny_center=65.1142
(16)    pdf2@binx_center=71.5708    pdf2@biny_center=72.7527
(17)    pdf2@binx_center=88.2035    pdf2@biny_center=80.3912
(18)    pdf2@binx_center=104.836    pdf2@biny_center=88.0297
(19)    pdf2@binx_center=121.469    pdf2@biny_center=95.6682
(20)    pdf2@binx_center=138.101    pdf2@biny_center=103.307
(21)    pdf2@binx_center=154.734    pdf2@biny_center=110.945
(22)    pdf2@binx_center=171.367    pdf2@biny_center=118.584
(23)    pdf2@binx_center=187.999    pdf2@biny_center=126.222
(24)    pdf2@binx_center=204.632    pdf2@biny_center=133.861

```
A simple contour plot could be generated by using the
```
wks  = gsn_open_wks ("x11","PDFX")
res  = True
res@gsnCenterString = "default 25 bins"
plot = gsn_csm_contour (wks, pdf2, res)

```

Example 2:

Have NCL calculate "nice" boundary bin values and spacing.

```  opt          = True
opt@bin_nice = True
pdf2 = pdfxy(x, y, 0, 0, opt)
```

Example 3:

More joint (bivariate) examples are at Probability Distributions