Log-normal Distribution Mode Calculator Log‑normal Distribution Mode Calculator For a log‑normal distribution where \(\ln(X) \sim N(\mu, \sigma^2)\), the mode is computed as: $$ \text{Mode} = \exp\bigl(\mu – \sigma^2\bigr). $$ * Enter the location parameter \(\mu\) and the scale parameter \(\sigma\) (with \(\sigma > 0\)). Step 1: Enter Parameters Location Parameter, \( \mu \): e.g., 0 […]
Log-normal Distribution Median Calculator Log‑normal Distribution Median Calculator For a log‑normal distribution where \(\ln(X) \sim N(\mu, \sigma^2)\), the median is: $$ \text{Median} = \exp(\mu). $$ * Enter the location parameter \(\mu\) (in practice, \(\mu\) is the mean of \(\ln(X)\)). Step 1: Enter Parameter Location Parameter, \( \mu \): e.g., 0 Calculate Median Calculated Median Median: […]
Log-normal Distribution Mean Calculator Log‑normal Distribution Mean Calculator For a log‑normal distribution with parameters \(\mu\) and \(\sigma\), the mean is given by: $$ E[X] = \exp\!\Bigl(\mu + \frac{\sigma^2}{2}\Bigr). $$ * Enter the location parameter \(\mu\) and the scale parameter \(\sigma\) (with \(\sigma > 0\)). Step 1: Enter Parameters Location Parameter, \( \mu \): e.g., 0 […]
Log-normal Distribution Inverse CDF Calculator Log-normal Distribution Inverse CDF Calculator For a log‑normal distribution with parameters \(\mu\) and \(\sigma\), the inverse CDF (quantile function) is: $$ Q(p; \mu, \sigma) = \exp\Bigl(\mu + \sigma\,\Phi^{-1}(p)\Bigr), $$ where \(\Phi^{-1}(p)\) is the inverse standard normal CDF. * Enter a probability \( p \) (with \( 0 < p < […]
Log-normal Distribution CDF Calculator Log-normal Distribution CDF Calculator For a log‑normal distribution with parameters \(\mu\) and \(\sigma\), the CDF is given by: $$ F(x;\mu,\sigma) = \Phi\!\Biggl(\frac{\ln(x)-\mu}{\sigma}\Biggr), $$ where \(\Phi(z)=0.5\Bigl[1+\operatorname{erf}\Bigl(\frac{z}{\sqrt{2}}\Bigr)\Bigr]\). * Enter a value for \( x \) (with \( x>0 \)), the location parameter \(\mu\), and the scale parameter \(\sigma>0\). Step 1: Enter Parameters \( […]
Log-normal Distribution PDF Calculator Log-normal Distribution PDF Calculator For a log‑normal distribution with parameters \(\mu\) and \(\sigma\), the PDF is given by: $$ f(x; \mu, \sigma) = \frac{1}{x\,\sigma\,\sqrt{2\pi}} \exp\!\Biggl(-\frac{(\ln x – \mu)^2}{2\sigma^2}\Biggr), \quad x > 0. $$ * Enter \( x \) (must be \(> 0\)), \(\mu\) (location parameter), and \(\sigma\) (scale parameter, \(\sigma > […]
T-Test Calculator T-Test Calculator Compute the t‑statistic and p‑value for a one‑sample t-test using: $$ t = \frac{\bar{x} – \mu_0}{SD/\sqrt{n}}. $$ * Enter the sample mean (\(\bar{x}\)), hypothesized mean (\(\mu_0\)), sample standard deviation (SD), sample size (\(n\)), and select one‑tailed or two‑tailed test. Step 1: Enter Test Data Sample Mean, \(\bar{x}\): e.g., 100 Hypothesized Mean, […]
Studentized Range Distribution Inverse CDF Calculator Studentized Range Distribution Inverse CDF Calculator This calculator finds the quantile \( q \) such that the Studentized Range CDF satisfies: $$ F(q; r, v)=p. $$ * Enter a probability \( p \) (0 < \( p \) < 1), number of groups \( r \) (\( r \ge […]
Studentized Range Distribution CDF Calculator Studentized Range Distribution CDF Calculator This calculator computes the cumulative probability for a Studentized Range distribution. The PDF is given by: $$ f(q; r, v)=\frac{2\,\Gamma\Bigl(\frac{v+1}{2}\Bigr)}{\sqrt{\pi}\,\Gamma\Bigl(\frac{v}{2}\Bigr)}\,r\,q^{v-1}\int_{0}^{\infty} t^{v}e^{-t^2}\Bigl[\Phi\Bigl(\frac{q}{2}+\frac{t}{\sqrt{2}}\Bigr)-\Phi\Bigl(\frac{t}{\sqrt{2}}-\frac{q}{2}\Bigr)\Bigr]^{r-2}dt. $$ * Enter the Studentized Range value \( q \) (q ≥ 0), number of groups \( r \) (integer, \( r \ge 2 […]