# Questions tagged [characteristic-function]

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### Characterizing clusters by separate feature vector scores

Say I have a medium amount of dependent variables in a study. These are scores from questionnaires that have been standardized so all are on a scale from 0 to 1. I have clusters of my patients - ...
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Let $\phi_1,\ldots,\phi_n$ denote characteristic functions for distributions on the real line. Let $a_1,\ldots,a_n$ denote nonnegative constants such that $a_1+\ldots+a_n = 1$. Show that $$\hspace{... 1answer 3k views ### How to find a density from a characteristic function? A distribution has the characteristic function$$\phi(t) = (1-t^2/2)\exp(-t^2/4),\ -\infty \lt t \lt \infty$$Show that the distribution is absolutely continuous and write the density function of ... 0answers 651 views ### Time series (stochastic process) estimating parameters using characteristic function I have a time series of assets {A_1, A_2, ..., A_n}, which is described by a sophisticated distribution having the following characteristic function: \phi(u; t;\theta), where \theta is a vector ... 1answer 2k views ### The mgf and cf of Student's t distribution A student's t distributed rv X has characteristic function but no moment generating function. I wonder if cf(X)=E[e^{itX}], why we cannot take t=-iu to get the mgf E[e^{uX}]? (This question ... 1answer 4k views ### Characteristic function and Fourier transform I understand the definition of characteristic functions used in probability theory: For a random Variable X with probability density function f_X the characteristic function is defined as:$$\...
Let us consider the following model: $$Y_j = X_j + \epsilon_j \hspace{15pt} j=1, ..., n$$ Where $Y_j$ is a noisy signal, $\epsilon_j$ is the noise which is independend from the signal $X_j$. We have ...