Hybrid lognormal distribution Calculator

Calculates the probability density function and lower and upper cumulative distribution functions of the hybrid lognormal distribution.

 Hybrid lognormal distribution is the distribution function changed the percentile "x" to "ln(x)+x " in the normal distribution function. It is also calculated by the random variable hyb(ρx)=ρx+ln(ρx) including the parameter ρ.
 percentile x x≧0 parameter ρ ρ＞0 mean μ of ρx+ln(ρx) standard deviation σ of ρx+ln(ρx), σ＞0
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Hybrid\ Lognormal\ distribution\ HybLogN(\rho x,\mu,\sigma)\\[10](1)\qquad probability\ density\\\hspace{30}f(x,\mu,\sigma)= {\large\frac{\rho}{\sqrt{2\pi}\sigma}(1+\frac{1}{\rho x})e^{-\frac{1}{2}\left(\frac{\rho x+ln(\rho x)-\mu}{\sigma}\right)^2}}\\[10](2)\qquad lower\ cumulative\ distribution\\\hspace{30}P(x,\mu,\sigma)={\large\int_{\small 0}^{\hspace{25}\small x}}f(t,\mu,\sigma)dt\\(3)\qquad upper\ cumulative\ distribution\\\hspace{30}Q(x,\mu,\sigma)={\large\int_{\small x}^{\hspace{25}\small\infty}}f(t,\mu,\sigma)dt\\(4)\ median:\ x_c={\large \frac{hyb^{-1}(\mu)}{\rho}}\\[10]\hspace{90} hyb(\rho x)=\rho x+ln(\rho x)=y\\\hspace{90} \rho x=hyb^{-1}(y)=cyb(y)\\$

Sending completion

To improve this 'Hybrid lognormal distribution Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired people Others
Useful?
Very Useful A little Not at All
Purpose of use?