Error Function (erf) Calculator Compute the error function: $$ \operatorname{erf}(x) \approx \operatorname{sgn}(x)\Bigl[1-\Bigl(a_1t + a_2t^2 + a_3t^3 + a_4t^4 + a_5t^5\Bigr)e^{-x^2}\Bigr], $$ where \( t=\frac{1}{1+0.3275911\,|x|} \). * Enter the value \( x \). Step 1: Enter \( x \) \( x \): e.g., 1 Calculate erf(x) Calculated Error Function \( \operatorname{erf}(x) \): Recalculate Approximation constants: \( […]
Read MoreInverse Complementary Error Function (erfc⁻¹) Calculator Inverse Complementary Error Function Calculator Compute the inverse complementary error function, \( \operatorname{erfc}^{-1}(y) \), where $$ \operatorname{erfc}(x)=1-\operatorname{erf}(x). $$ * Enter a value \( y \) (with \(0 < y < 2\)). Step 1: Enter \( y \) \( y \) (erfc value): Enter a value between 0 and 2 […]
Read MoreInverse Error Function (erf⁻¹) Calculator Inverse Error Function (erf⁻¹) Calculator Value of y (-1 < y < 1): Calculate erf⁻¹(y) Reset
Read MoreComplementary Error Function (erfc) Calculator Complementary Error Function (erfc) Calculator The complementary error function is defined as $$ \operatorname{erfc}(x)=1-\operatorname{erf}(x). $$ * Enter the value of \( x \). Step 1: Enter \( x \) \( x \): e.g., 1 Calculate \( \operatorname{erfc}(x) \) Calculated Complementary Error Function \( \operatorname{erfc}(x) \): Recalculate Formula: \( \operatorname{erfc}(x)=1-\operatorname{erf}(x) \)
Read MoreConditional Probability Calculator Conditional Probability Calculator Select Operation: Calculate P(A|B)Calculate P(A ∩ B) Calculate Reset
Read MoreUnion Probability Calculator Union Probability Calculator Select Calculation Type: Calculate P(A ∪ B) using P(A), P(B), and P(A ∩ B)Calculate P(A ∪ B) for Independent EventsCalculate P(A ∪ B) for Mutually Exclusive Events Calculate P(A ∪ B) Reset
Read MoreCritical F-value Calculator Critical F-value Calculator Degrees of Freedom (df₁ – Numerator): Degrees of Freedom (df₂ – Denominator): Significance Level (α): Calculate Critical F-value Reset
Read MoreLog-normal Distribution Calculator Log-normal Distribution Calculator For parameters \(\mu\) and \(\sigma\) (with \(\sigma>0\)), the PDF is: $$ f(x) = \frac{1}{x\,\sigma\sqrt{2\pi}} \exp\Bigl(-\frac{(\ln x – \mu)^2}{2\sigma^2}\Bigr),\quad x>0. $$ and the CDF is: $$ F(x) = \frac{1}{2}\Bigl[1 + \operatorname{erf}\Bigl(\frac{\ln x – \mu}{\sigma\sqrt{2}}\Bigr)\Bigr],\quad x>0. $$ Step 1: Enter Parameters \(\mu\): Enter a real number (e.g., 0) \(\sigma\) (σ > […]
Read MoreYou can use our calculators to calculate the probability density function (PDF) or cumulative distribution function (CDF) of the F-distribution F Distribution Calculator F Distribution Calculator For degrees of freedom \(d_1>0\) and \(d_2>0\), the PDF is: $$ f(x;d_1,d_2)=\frac{\Gamma\Bigl(\frac{d_1+d_2}{2}\Bigr)}{\Gamma\Bigl(\frac{d_1}{2}\Bigr)\Gamma\Bigl(\frac{d_2}{2}\Bigr)}\Bigl(\frac{d_1}{d_2}\Bigr)^{\frac{d_1}{2}}x^{\frac{d_1}{2}-1}\Bigl(1+\frac{d_1}{d_2}x\Bigr)^{-\frac{d_1+d_2}{2}}, \quad x>0. $$ and the CDF is: $$ F(x;d_1,d_2)=I_{\frac{d_1x}{d_1x+d_2}}\Bigl(\frac{d_1}{2},\frac{d_2}{2}\Bigr), \quad x>0. $$ Mean exists if \(d_2>2\) and […]
Read MoreTotal Effect Calculator for Mediation Models Total Effect Calculator for Mediation Models Path Coefficient a (X → M): Path Coefficient b (M → Y): Direct Effect (c’ – X → Y, excluding M): Calculate Total Effect Reset
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