﻿ g01mb Method
g01mb returns the reciprocal of Mills' Ratio.

# Syntax

C#
```public static double g01mb(
double x
)```
Visual Basic
```Public Shared Function g01mb ( _
x As Double _
) As Double```
Visual C++
```public:
static double g01mb(
double x
)```
F#
```static member g01mb :
x : float -> float
```

#### Parameters

x
Type: System..::..Double
On entry: $x$, the argument of the reciprocal of Mills' Ratio.

#### Return Value

g01mb returns the reciprocal of Mills' Ratio.

# Description

g01mb calculates the reciprocal of Mills' Ratio, the hazard rate, $\lambda \left(x\right)$, for the standard Normal distribution. It is defined as the ratio of the ordinate to the upper tail area of the standard Normal distribution, that is,
 $λx=ZxQx=12πe-x2/212π∫x∞e-t2/2dt.$
The calculation is based on a Chebyshev expansion as described in s15ag.

# References

Gross A J and Clark V A (1975) Survival Distributions: Reliability Applications in the Biomedical Sciences Wiley

None.

# Accuracy

In the left-hand tail, $x<0.0$, if $\frac{1}{2}{e}^{-\left(1/2\right){x}^{2}}\le \text{}$ the safe range parameter (x02am), then $0.0$ is returned, which is close to the true value.
The relative accuracy is bounded by the effective machine precision. See s15ag for further discussion.

# Parallelism and Performance

None.

If, before entry, $x$ is not a standard Normal variable, it has to be standardized, and on exit, g01mb has to be divided by the standard deviation. That is, if the Normal distribution has mean $\mu$ and variance ${\sigma }^{2}$, then its hazard rate, $\lambda \left(x;\mu ,{\sigma }^{2}\right)$, is given by
 $λx;μ,σ2=λx-μ/σ/σ.$

# Example

The hazard rate is evaluated at different values of $x$ for Normal distributions with different means and variances. The results are then printed.

Example program (C#): g01mbe.cs

Example program data: g01mbe.d

Example program results: g01mbe.r