Question

I may just be being brain dead, but I have code which defines a lognormal class for manipulation in Python using Scipy.stats.

My class looks like this:

class LogNorm :

def __init__(self, mean, sd, offset=0) :
# uses 'real' units -i.e., 100000, 15000 for mean and sdn
    self.mean = mean
    self.sd = sd
    self.offset = offset
    self.xvar_mu, self.xvar_sigma = get_base_mu_and_sigma(mean, sd)
    self.mean = np.exp(self.xvar_mu + self.xvar_sigma**2.0/2.0)   # reflect that change in the Y 
    self.sd = ((np.exp(self.xvar_sigma**2.0) - 1.0) *
               (np.exp(2.0 * self.xvar_mu + self.xvar_sigma**2.0))) ** 0.5
    self.RV = lognorm(s = self.xvar_sigma, scale = self.mean, loc = self.offset)  # fozen

The idea here is you pass in the mean and sd, as measured, of the lognormal itself. I record those for posterity (assume offset = 0.0, as per the default). Then I have a helper function which maps those into the mu and sigma of the normal distribution that underlies the lognormal. That function looks like so, if useful:

def get_base_mu_and_sigma(mean, sd) :
    mu = math.log(mean**2.0 / (sd**2.0 + mean**2.0)**0.5)
    sigma = (math.log(1.0 + sd**2.0/mean**2.0))**0.5
    return (mu, sigma)

This comes straight from Wikipedia, and seems right (check out the end of the 'Arithmetic Moments' section): https://en.wikipedia.org/wiki/Log-normal_distribution

Then, 'self.RV' becomes a 'frozen' RV, and has a bunch of builtin/inherited functions (mean(), median(), var(), etc) related to the lognormal described by mu and sigma.

The challenge I have is that when I create such an object, and then try examining the mean and sd (via square root of the variance), the numbers don't seem to match. For example, using mean = 110517.09 and sd = 2210.34 (from my application), when I then execute the following code I get inconsistent answers:

        p = rv1.RV.pdf(x)
        print("rv1.mean, rv1.sd = " + str(rv1.mean) + "  " + str(rv1.sd))
        print("rv1.mean(), rv1.var()**0.5 = " + str(rv1.RV.mean()) + "  " + str(rv1.RV.var()**0.5))

gives:

rv1.mean, rv1.sd = 110517.09180756475  2210.341836151173
rv1.mean(), rv1.var()**0.5 = 110539.19301602637  2210.783860320406

Any clue what I am doing wrong?

Answer 1

您使用self.mean作为scale的{{1}}参数，但这不正确。引自docstring for lognorm：

对数正态随机变量scipy.stats.lognorm的常见参数化是根据唯一正态分布随机变量{{1}的均值Y和标准差mu计算的。这样exp（X）= Y.这个参数化对应于设置sigma和X。

因此，当您通过调用s = sigma创建scale = exp(mu)时，self.RV参数必须为lognorm。（这假定scale为0。）

这是一个使用函数np.exp(self.xvar_mu)转换参数的简化示例。

首先，这是您的函数，以及您使用的示例值：

offset

获取基础正态分布的参数：

get_base_mu_and_sigma

创建scipy In [154]: def get_base_mu_and_sigma(mean, sd) : ...: mu = math.log(mean**2.0 / (sd**2.0 + mean**2.0)**0.5) ...: sigma = (math.log(1.0 + sd**2.0/mean**2.0))**0.5 ...: return (mu, sigma) ...: In [155]: mean = 110517.09180756475 In [156]: sd = 2210.341836151173发布的实例，并验证该发布的平均值和标准差与In [157]: mu, sigma = get_base_mu_and_sigma(mean, sd)和lognorm匹配：

mean

Am I doing something wrong when using Scipy.stats when implementing a lognormal function?

1 个答案: