LambertW0 / lambertWm1 in the lamW package it returnsĬorless, R. W returns numeric, Inf (for z = Inf), or NA if \log W'(z) = \log W(z) - \log z - \log (1 + W(z))įor this reason it is numerically faster to pass the value of W(z) asĪn argument to deriv_W since W(z) often has already been
![derivative of log z derivative of log z](https://d2vlcm61l7u1fs.cloudfront.net/media%2F7cc%2F7cc01e55-4e95-4534-ad30-f42ae2b57f84%2Fphp3mvbFG.png)
Moreover, by taking logs on both sides we can even simplify further to Similarly, theĭerivative can be expressed as a function of W(z): This can be doneĮfficiently since \log W(z) = \log z - W(z). Log_W computes the natural logarithm of W(z). Lambert W function evaluated at z see Details below forĭepending on the argument z of W(z) one can distinguish 3 cases:īranch = 0)) and non-principal ( W(z, branch = -1)) branch z < -1/e W ( z, branch = 0 ) deriv_W ( z, branch = 0, W.z = W ( z, branch = branch )) log_deriv_W ( z, branch = 0, W.z = W ( z, branch = branch )) deriv_log_W ( z, branch = 0, W.z = W ( z, branch = branch )) log_W ( z, branch = 0, W.z = W ( z, branch = branch ))Ī numeric vector of real values note that W(Inf, branch = 0)Įither 0 or -1 for the principal or non-principal xexp: Transformation that defines the Lambert W function and its.W_gamma: Inverse transformation for skewed Lambert W RVs.W_delta: Inverse transformation for heavy-tail Lambert W RVs.W: Lambert W function, its logarithm and derivative.U-utils: Zero-mean, unit-variance version of standard distributions.theta-utils: Utilities for the parameter vector of Lambert W\times F.test_symmetry: Test symmetry based on Lambert W heavy tail(s).test_normality: Visual and statistical Gaussianity check.tau-utils: Utilities for transformation vector tau.MLE_LambertW: Maximum Likelihood Estimation for Lambert W \times F.medcouple_estimator: MedCouple Estimator remembering that z wX +b and we are trying to find derivative of the function w.r.t b, if we take the derivative w.r.loglik-LambertW-utils: Log-Likelihood for Lambert W\times F RVs.LambertW-utils: Utilities for Lambert W \times F Random Variables.LambertW-toolkit: Do-it-yourself toolkit for Lambert W \times F distribution \begingroup I know the that 1/z is holomorphic on punctured plane but for example in real plane, when a function is differentiable at a point, it's continuous at at that point, like wise, 1/z is a derivative of log(z) and it's continuous on negative axis except at origin, but the function log z is not continous at (-inf,0.LambertW-package: R package for Lambert W \times F distributions.LambertW_input_output-methods: Methods for Lambert W input and output objects.LambertW_fit-methods: Methods for Lambert W\times F estimates.ks.test.t: One-sample Kolmogorov-Smirnov test for student-t distribution.IGMM: Iterative Generalized Method of Moments - IGMM.get_support: Computes support for skewed Lambert W x F distributions.get_output: Transform input X to output Y.Your map Z ( a) a X + ( 1 a) Y is a well-defined map from an open set in a Banach space to a Banach space, Z: R L 1. G_delta_alpha: Heavy tail transformation for Lambert W random variables Yes, it makes sense if for example your random variables are in L 1.Gaussianize: Gaussianize matrix-like objects.gamma_Taylor: Estimate gamma by Taylor approximation.gamma_01: Input parameters to get a zero mean, unit variance output for.
![derivative of log z derivative of log z](https://i.stack.imgur.com/AtfiF.png)
estimate-moments: Skewness and kurtosis.distname-utils: Utilities for distributions supported in this package.deprecated-functions: List of deprecated functions.delta_Taylor: Estimate of delta by Taylor approximation with derivative equal to (z a)-1 hence the FTC Theorem 17.1 does not apply, the actual evaluation 2i was done in the previous lecture.delta_01: Input parameters to get zero mean, unit variance output given.common-arguments: Common arguments for several functions.bootstrap: Bootstrap Lambert W x F estimates.beta-utils: Utilities for parameter vector beta of the input distribution.analyze_convergence: Analyze convergence of Lambert W estimators.A useful mathematical differentiation calculator to simplify the functions. Ensure that the input string is as per the rules specified above.Īn online derivative calculator that differentiates a given function with respect to a given variable by using analytical differentiation. Use inv to specify inverse and ln to specify natural log respectivelyĦ. Write sinx+cosx+tanx as sin(x)+cos(x)+tan(x)Ĥ. Use paranthesis() while performing arithmetic operations.Įg:1. Use ^(1/2) for square root ,'*' for multiplication, '/' for division, '+' for addition, '-' for subtraction.ģ.