PSDEV

Type:

Command

 

 

 

 

 

Description:

Population Standard Deviation Command: Calculates the population standard deviation of each

 

of the m columns of coordinate values in the current statistics matrix (reserved variable ΣDAT).

 

PSDEV returns a vector of m real numbers, or a single real number if m = 1. The population

 

standard deviation is computed using this formula:

 

 

 

 

1

n

(xk – x)

2

 

 

 

 

--

∑

 

 

 

 

 

nk = 1

 

 

 

 

where xk is the kth coordinate value in a column, x is the mean of the data in this column, and n

 

is the number of data points.

 

 

 

 

Access:

…µPSDEV

 

 

 

 

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 1/Argument 1

 

Level 1/Item 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

→

xpsdev

 

 

 

 

 

 

→

[ xpsdev1 xpsdev2 ... xpsdevm }

 

 

 

 

 

See also:

MEAN, PCOV, PVAR, SDEV, TOT, VAR

 

 

 

 

 

 

 

 

 

 

PSI

Function

 

 

 

 

 

Type:

 

 

 

 

 

Description:

Calculates the polygamma function, the nth derivative of the digamma function, at a point a.

 

PSI(a, 0) is equivalent to Psi(a).

 

 

 

 

Access:

!´LSPECIAL

 

 

 

 

Input:

Level 2/Argument 1: A real or complex expression specifying the point a.

 

Level 1/Argument 2: A non-negative integer, n.

 

Output:

The value of the polygamma function PSI(a, n).

 

Flags:

Exact mode must be set (flag –105 clear), and

 

 

numeric mode must not be set (flag –3 clear), if symbolic results are wanted.

 

Complex mode must be set (flag –103 set) if a complex value is used for point a.

See also:

Psi

 

 

 

 

 

Psi

Function

 

 

 

 

 

Type:

 

 

 

 

 

Description:

Calculates the digamma function at a point a. The digamma function is the derivative of the

 

natural logarithm (ln) of the gamma function. The function can be represented as follows:

 

d

Γ′(z)

 

 

 

 

 

Ψ(z) = -----( ln Γ(z))

= ------------

 

 

 

 

 

dz

Γ(z)

 

 

 

 

Access:

!´LSPECIAL

 

 

 

 

Input:

A real or complex expression specifying the point a.

 

Output:

The digamma function at the specified point.

 

 

Flags:

Exact mode must be set (flag –105 clear), and

 

 

numeric mode must not be set (flag –3 clear), if symbolic results are wanted. For example, with

 

these settings, Psi(3) evaluates to the symbolic value Psi(3).

 

 

Complex mode must be set (flag –103 set) if a complex value is used for point a.

See also:

PSI

 

 

 

 

 

Full Command and Function Reference 3-181