pyrcel.distributions
.Lognorm¶
- class pyrcel.distributions.Lognorm(mu, sigma, N=1.0, base=2.718281828459045)¶
Lognormal size distribution.
An instance of
Lognorm
contains a construction of a lognormal distribution and the utilities necessary for computing statistical functions associated with that distribution. The parameters of the constructor are invariant with respect to what length and concentration unit you choose; that is, if you use meters formu
and cm**-3 forN
, then you should keep these in mind when evaluating thepdf()
andcdf()
functions and when interpreting moments.- Parameters:
- mufloat
Median/geometric mean radius, length unit.
- sigmafloat
Geometric standard deviation, unitless.
- Nfloat, optional (default=1.0)
Total number concentration, concentration unit.
- basefloat, optional (default=np.e)
Base of logarithm in lognormal distribution.
- Attributes:
- median, meanfloat
Pre-computed statistical quantities
Methods
pdf(x)
Evaluate distribution at a particular value
cdf(x)
Evaluate cumulative distribution at a particular value.
moment(k)
Compute the k-th moment of the lognormal distribution.
- __init__(mu, sigma, N=1.0, base=2.718281828459045)¶
- cdf(x)¶
Cumulative density function
\[\text{CDF} = \frac{N}{2}\left(1.0 + \text{erf}(\frac{\log{x/\mu}}{\sqrt{2}\log{\sigma}}) \right)\]- Parameters:
- xfloat
Ordinate value to evaluate CDF at
- Returns:
- value of CDF at ordinate
- invcdf(y)¶
Inverse of cumulative density function.
- Parameters:
- yfloat
CDF value, between (0, 1)
- Returns:
- value of ordinate corresponding to given CDF evaluation
- moment(k)¶
Compute the k-th moment of the lognormal distribution
\[F(k) = N\mu^k\exp\left( \frac{k^2}{2} \ln^2 \sigma \right)\]- Parameters:
- kint
Moment to evaluate
- Returns:
- moment of distribution
- pdf(x)¶
Probability density function
\[\text{PDF} = \frac{N}{\sqrt{2\pi}\log\sigma x}\exp\left( -\frac{\log{x/\mu}^2}{2\log^2\sigma} \right)\]- Parameters:
- xfloat
Ordinate value to evaluate CDF at
- Returns:
- value of CDF at ordinate
- stats()¶
Compute useful statistics for a lognormal distribution
- Returns:
- dict
Dictionary containing the stats
mean_radius
,total_diameter
,total_surface_area
,total_volume
,mean_surface_area
,mean_volume
, andeffective_radius