Uniform Distribution Mode Calculator Uniform Distribution Mode Calculator For a uniform distribution over the interval \([a,b]\), the probability density function (PDF) is constant: $$ f(x;a,b)=\begin{cases} \frac{1}{b-a}, & a\le x\le b, \\ 0, & \text{otherwise.} \end{cases} $$ * Since every value between \(a\) and \(b\) has the same probability, there is no unique mode. Step 1: […]
Read MoreUniform Distribution Median Calculator Uniform Distribution Median Calculator For a uniform distribution over the interval \([a, b]\), the median is given by: $$ m = \frac{a+b}{2}. $$ * Enter the minimum value \(a\) and maximum value \(b\) (with \(a < b\)). Step 1: Enter Parameters Minimum, \(a\): e.g., 0 Maximum, \(b\): e.g., 10 (must be […]
Read MoreUniform Distribution Mean Calculator Uniform Distribution Mean Calculator For a uniform distribution over the interval \([a,b]\), the mean is: $$ \mu = \frac{a+b}{2}. $$ * Enter the minimum value \(a\) and maximum value \(b\) (with \(a < b\)). Step 1: Enter Parameters Minimum, \(a\): e.g., 0 Maximum, \(b\): e.g., 10 (must be greater than \(a\)) […]
Read MoreUniform Distribution Inverse CDF Calculator Uniform Distribution Inverse CDF Calculator For a uniform distribution over the interval \([a, b]\), the inverse CDF (quantile function) is: $$ Q(p; a, b)=a+p\,(b-a), \quad 0 \le p \le 1. $$ * Enter the minimum value \(a\), maximum value \(b\) (with \(a
Read MoreUniform Distribution CDF Calculator Uniform Distribution CDF Calculator For a uniform distribution over the interval \([a,b]\), the CDF is given by: $$ F(x;a,b)= \begin{cases} 0, & x < a, \\\\ \frac{x-a}{b-a}, & a \le x \le b, \\\\ 1, & x > b. \end{cases} $$ * Enter the minimum value \(a\), maximum value \(b\) (with […]
Read MoreUniform Distribution PDF Calculator Uniform Distribution PDF Calculator For a uniform distribution over the interval \([a,b]\), the PDF is given by: $$ f(x;a,b)= \begin{cases} \frac{1}{b-a}, & a \le x \le b, \\ 0, & \text{otherwise.} \end{cases} $$ * Enter the minimum value \(a\), maximum value \(b\) (with \(a < b\)), and a value \(x\) for […]
Read MoreNegative Binomial Distribution Variance Calculator Negative Binomial Distribution Variance Calculator For a negative binomial distribution (the number of failures \(X\) before the \(r\)th success) with failure probability \(p\) (and success probability \(1-p\)), the variance is given by: $$ \sigma^2 = \frac{r\,p}{(1-p)^2}. $$ * Enter the number of successes \(r\) (integer \(\ge 1\)) and the failure […]
Read MoreNegative Binomial Distribution Sample Generator Negative Binomial Distribution Sample Generator This generator produces random samples from a negative binomial distribution defined as the number of failures \(X\) before the \(r\)th success, where the probability of success is \(1-p\) (and the failure probability is \(p\)). Samples are generated by simulating Bernoulli trials until \(r\) successes occur. […]
Read MoreWeibull Distribution Mode Calculator Weibull Distribution Mode Calculator For a Weibull distribution with shape parameter \( k \) and scale parameter \( \lambda \): If \( k \le 1 \): Mode = 0; If \( k > 1 \): $$ \text{Mode} = \lambda \left(\frac{k-1}{k}\right)^{\frac{1}{k}}. $$ * Enter the shape parameter \( k \) (with \( […]
Read MoreNegative Binomial Distribution Median Calculator Negative Binomial Distribution Median Calculator For a negative binomial distribution defined as the number of failures \(X\) before the \(r\)th success with failure probability \(p\), the CDF is: $$ F(X \le x)=\sum_{i=0}^{x} \binom{i+r-1}{i}(1-p)^r p^i, \quad x=0,1,2,\dots $$ The median is defined as the smallest integer \(m\) such that \(F(m)\ge0.5\). * […]
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