# Hybrid lognormal distribution (chart) Calculator

## Calculates a table of the probability density function, or lower or upper cumulative distribution function of the hybrid lognormal distribution, and draws the chart.

 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.
select function
 probability density f lower cumulative distribution P upper cumulative distribution Q
parameter ρ
 ρ＞0
mean μ
 of ρx+ln(ρx)
standard deviation σ
 of ρx+ln(ρx), σ＞0
[ initial percentile x
 x≧0
increment
 repetition ]
 $\normal Hybrid\ Lognormal\ distribution\ HybLogN(\rho x,\mu,\sigma)\\[10](1)\qquad probability\ density\\\hspace{30}f(x,\mu,\sigma)= {\large\frac{\rho}{\sqrt{2\pi}\sigma}(1+\frac{1}{\rho x})e^{-\frac{1}{2}\left(\frac{\rho x+ln(\rho x)-\mu}{\sigma}\right)^2}}\\[10](2)\qquad lower\ cumulative\ distribution\\\hspace{30}P(x,\mu,\sigma)={\large\int_{\small 0}^{\hspace{25}\small x}}f(t,\mu,\sigma)dt\\(3)\qquad upper\ cumulative\ distribution\\\hspace{30}Q(x,\mu,\sigma)={\large\int_{\small x}^{\hspace{25}\small\infty}}f(t,\mu,\sigma)dt\\(4)\ median:\ x_c={\large \frac{hyb^{-1}(\mu)}{\rho}}\\[10]\hspace{90} hyb(\rho x)=\rho x+ln(\rho x)=y\\\hspace{90} \rho x=hyb^{-1}(y)=cyb(y)\\$

Thank you for your questionnaire.
Sending completion

To improve this 'Hybrid lognormal distribution (chart) 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?
Comment/Request (Click here to report a bug).Bug report (Click here to report questionnaire.）
Calculation bug(Please enter information such as specific input values, calculation result, correct result, and reference materials (URL and documents).)
Text bug(Please enter information such as wrong and correct texts)
Your feedback and comments may be posted as customer voice.