Normal Distribution PDF Calculator

Calculates the normal distribution probability density function.

See the Statistical Distributions Overview page for more statistical distribution calculators.

Example 1

Assess the density of observing a 0% return on a stock that typically averages a 0.05% return with a volatility (standard deviation) of 1.2%

Value	Keystrokes	Display	Description
0	x	0.00	Stores the x value.
.05	μ	0.0500	Stores the mean value.
1.2	σ	1.20	Stores the standard deviation value.
	pdf	0.332	Calculates the probability density function

The History Detail

Normal Distribution PDF
           0.00 : The x value.
         0.0500 : The mean of the distribution.
           1.20 : The standard deviation of the distribution.
          0.332 : The normal distribution probability density function.
Result:	 0.332
	

Example 2

A financial analyst has observed that the density of a stock's return distribution at 0.5% is 0.30, with a known standard deviation of 1.2%. Using this information, determine the stock's average daily return.

Value	Keystrokes	Display	Description
.3	pdf	0.3000	Stores the pdf value.
.5	x	0.500	Stores the x value.
1.2	σ	1.20	Stores the standard deviation value.
	μ	-0.0439	Solves for the mean value.

The History Detail

Normal Distribution PDF
Solving for μ, mean of the distribution, with initial value (guess) of 0.0500
          0.500 : The x value.
        -0.0439 : The mean of the distribution.
           1.20 : The standard deviation of the distribution.
          0.300 : The normal distribution probability density function.
Result:	 -0.0439
	

Reference:

Normal distribution - Wikipedia