1.3. EDA Techniques
1.3.6. Probability Distributions
1.3.6.6. Gallery of Distributions
1.3.6.6.14. |
Power Lognormal Distribution |
where p (also referred to as the power parameter)
and 
are the
shape parameters,
is the cumulative
distribution function of the standard normal
distribution, and 
is the probability
density function of the standard normal
distribution.
As with other probability distributions, the power lognormal
distribution can be transformed with a location
parameter, 
, and a
scale parameter, B.
We omit the equation for the general form of the power lognormal
distribution. Since the general form of probability functions can be
expressed in terms of the standard
distribution, all subsequent formulas in this section are
given for the standard form of the function.
The following is the plot of the power lognormal probability density
function with four values of p and
set to 1.
where is the cumulative
distribution function of the standard normal
distribution.
The following is the plot of the power lognormal cumulative distribution function with the same values of p as the pdf plots above.
where 
is the percent point
function of the standard normal distribution.
The following is the plot of the power lognormal percent point function with the same values of p as the pdf plots above.
where is the cumulative
distribution function of the standard normal distribution, and
is the probability density
function of the standard normal distribution.
Note that this is simply a multiple (p) of the lognormal hazard function.
The following is the plot of the power lognormal hazard function with the same values of p as the pdf plots above.
The following is the plot of the power lognormal cumulative hazard function with the same values of p as the pdf plots above.
The following is the plot of the power lognormal survival function with the same values of p as the pdf plots above.
The following is the plot of the power lognormal inverse survival function with the same values of p as the pdf plots above.
