Questions tagged [inverse-gaussian-distrib]

A right skew continuous probability distribution on positive real numbers.

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34 views

The inverse cumulative distribution of the product of two normally distributed variables

Let me preface this by saying that I am not in any sense a statistician and I might be going about this totally wrong… I am interested in calculating the inverse cumulative distribution of the ...
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0answers
36 views

Modelling Inverse Gaussian Distribution for Survival Data in R

I am fitting survival data with different distributions in order to determine what best characterises my data. I believe that the inverse gaussian distribution may be a good fit but I have been having ...
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0answers
34 views

Inverse Gaussian Distribution and the Central Limit Theorem

Let the random variables $Y_1,\ldots,Y_n$ be independent and identically distributed (i.i.d.) (standard) Inverse Gaussian random variables with parameters $\mu$ and $\lambda$. Then, let the random ...
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47 views

Minimum of n independent, but not identically distributed inverse Gaussians

I would like to find the probability distribution of the minimum of of n independent, but not identically distributed, i.e. differently parametrized inverse Gaussians. I would prefer an analytical ...
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2answers
3k views

Do test scores really follow a normal distribution?

I've been trying to learn which distributions to use in GLMs, and I'm a little fuzzled on when to use the normal distribution. In one part of my textbook, it says that a normal distribution could be ...
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0answers
118 views

How to get the prediction std using Gaussian Process in Scikit-Learn

I'm fitting some data using Gaussian Process (GP) in Scikit-Learn. As I understand, the GP requires to scale both X (input features) and Y (outputs) to standard normal distribution (mean = 0 and std = ...
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45 views

Transformation the inverse Gaussian probability distribution

Suppose $X$ has pdf $I(\mu, \tau)$ with density, $$\sqrt{\frac{\tau}{2\pi x^{3}}}\exp\{-\frac{\tau}{2x\mu^{2}}(x-\mu)^2\}\quad; x>0, \quad \tau,\mu>0$$ I want to find the distribution of $V = \...
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711 views

Fitting GLM (family = inverse.gaussian) on simulated AR(1)-data

I am encountering quite an annoying and to me incomprehensible problem, and I hope some of you can help me. I am trying to estimate the autoregression (influence of previous measurements of variable X ...
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1answer
583 views

Exponential Family with Dispersion Parameter Distributions

Defining the exponential dispersion family by $exp\left(\frac{x_{i}\theta - b(\theta_{i})}{\phi} + c(x_{i}, \phi, w_{i})\right)$ I'd like to change the usual Inverse-Gaussian density below to the ...
2
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1answer
85 views

Deriving Inverse Gaussian as First Passage Time of Wiener Process

Chhikara and Folks (1988) show that the inverse gaussian distribution arises as the first passage time for a wiener process. However, there are several steps I don't quite understand. In particular, ...
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2answers
1k views

Python: Gaussian Copula or inverse of cdf

Let's say I have a column x with uniform distributed values. To these values, I applied a cdf-function. Now I want to calculate the Gaussian Copula, but I can't find the function in python. I read ...
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288 views

GLMM inverse gaussian and treatment contrasts (response times)

I've been trying to analyse a dataset of response times following Lo & Andrews' (2015) proposal here: https://doi.org/10.3389/fpsyg.2015.01171 They propose using a GLMM that assumes a Gamma or ...
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2answers
498 views

Which Single Summary Statistic to use for Inverted Bell Curve (Bimodal Distribution)?

I've collected some datasets for which I want to report a summary statistic. I produced normal probability plots for the datasets, and the data does not conform to a Gaussian distribution - there are ...
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35 views

Gaussian Bivariate Copulas Inconsistent Reasoning

While studying Gaussian copulas, I have stumbled accross a question which seems to result from wrong reasoning. In the arguments below, where have I gone wrong? Let $c(u, v)$ denote the density of ...
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1answer
68 views

Distributions with undefined parameters

I am studying the Bayesian Lasso and noticed something interesting on Page 682 at the bottom of the second column here Some background: a hierarchical setup for data $X, y$, regression coefficients, $...
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1answer
155 views

How to apply glm(generalized linear model) in this simple example?

We are given 1) Y = $(Y_1,Y_2,...,Y_n)^T$ ~ Exponential 2) E[Y] = $\mu$ = X$\beta$, where X $\in R^{nxr}$ and $\beta \in R^r$ My question is can we apply the glm in this case? The case where the ...
3
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0answers
329 views

Expectation of log(1/X) when X follows inverse gaussian distribution

Can anybody help me in this question? How to derive the expectation of log(1/X) when X follows inverse Gaussian distribution? Found out a type of approximation for $\mathbb{E}[\log(X)]$ while $X \sim ...
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0answers
298 views

Interpretation of Generalized Inverse Gaussian regression with GAMLSS

Background on my project: I am comparing proteins (nodes) between a network representing protein interactions in metastatic patients v/s another network representing protein interactions in non-...
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293 views

How to calculate E(1/Y) when Y is Inverse Gaussian distributed?

The Inverse Gaussian Distribution density is : $$\frac{\phi^{\frac{1}{2}}}{\sqrt{2\pi y^3}} exp[\frac{-\phi(y - \mu)^2}{2\mu^2y}]$$ Got to this integral: $$\int_0^\infty \frac{1}{y} \frac{\phi^{\frac{...
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548 views

Sufficient Statistic for inverse Gaussian Distribution

Let $X_1,...,X_n$ be a random sample from population with the pdf of the inverse Gaussian distribution $$f(x|\theta,\beta)=(\frac{\beta}{2 \pi x^3})^\frac{1}{2}e^{-\frac{\beta(x-\theta)^2}{2\...
3
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0answers
193 views

Specifying distribution in generalized estimating equation GEE

GEE allows you to identify the distribution of the outcome variable and appropriate link function. How do you make this selection in a longitudinal model where the distribution changes in time. An ...
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0answers
224 views

Testing GLMM residuals against specific families and link functions (R)

When running a GLMM in R with family=gaussian and link=identity, it's easy enough to test whether normality and homoscedasticity ...
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2answers
453 views

Is there a package for three parameter inverse gaussian or lognormal distributions in C++?

I want to generate random numbers from one of the following distribution in C++. I haven't been able to find any libraries though. Do they exist? In order of preference: Three parameter inverse ...
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147 views

Conditional inverse Gaussian distribution

I am considering the Inverse Gaussian distribution as the hitting time distribution for a Wiener process, $W(t)$, with drift parameter $\nu$ and variance parameter $\sigma$. Define the hitting time as ...