Questions tagged [inverse-gaussian-distrib]

A right skew continuous probability distribution on positive real numbers.

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Distribution of $\frac{1}{1+Y}$ if $Y$ is Normally Distributed [duplicate]

Suppose $Y\sim N(\mu,\sigma)$ I would like to investigate the distribution of: $$\frac{1}{1+Y}$$ Does the distribution exist and is it well defined? Does it have analytically computable moments? ...
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Fitting GLMMs for RT data with different condition level distributions

I have RT data that I'm looking to analyse. RT data usually follows Gamma/Inverse-Gaussian shape distributions, thus I usually fit a glmer model (in R) specifying the family as either of those ...
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1answer
61 views

Can't compute CDF for Inverse Gaussian distribution

I am trying to implement in Python the CDF of the Inverse Gaussian distribution: Inverse Gaussian pdf: $$ f(x) = \sqrt{\frac{\lambda}{2\pi x^3}}e^{-\frac{\lambda(x-\mu)^2}{2\mu^2x}} $$ Inverse ...
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172 views

Inverse Gaussian chi square connection

The inverse Gaussian distribution $IG(\mu,\lambda)$ is associated with the density $$f(x;\mu,\lambda) = \sqrt{\frac{\lambda}{2\pi x^3}}\,\exp\left\{-\frac{\lambda(x-\mu)^2}{2\mu^2x}\right\}\qquad \...
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Which data visualization when running GLMM?

I'm analysing correct response rate and response time of participants on a task. For the first one, I ran a mixed effect logistic regression: ...
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1answer
57 views

How to choose a prior : family for a response with negative values?

I’m modeling percentage change in oxygen levels in the blood from a particular experiment. So my prior before seeing the data was an inverse gaussian distribution. But my data (response variable ) has ...
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62 views

P-values and confidence intervals for Inverse Gaussian GLMM?

I want to test the effects of different variables on Reaction Times data. Following the recommendations of Lo & Andrews (2015) I compared the AIC/BIC of three GLMM with a Gaussian, a Gamma and an ...
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1answer
89 views

Jacobian of Inverse Gaussian Transformation in Schwarz & Samanta (1991)

In the sample size $n=2$ case when transforming $\{x_1, x_2\}$ to $\{\bar{x}, s\}$ (where $X_1, X_2 \overset{iid}{\sim} IG(\mu, \lambda)$, $\bar{X}=\frac{\sum_i^2 X_i}{n}$, and $S=\sum_i^2 (\frac{1}{...
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3k views

Speed in m/s is normally distributed, but same data expressed as “Time for 10 meters” is not

I am trying to understand why the same data can be normally distributed if expressed in one way, but not normally distributed if expressed in another way. I have a variable that is "time taken to ...
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40 views

CDF for inverse normal distribution [duplicate]

Do you have any idea how I can get the cumulative distribution function (CDF) for inverse-normal (Gauusian) distribution? Modeler 18.2 doesn't have that specific function, and I need it to calculate a ...
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68 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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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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67 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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3answers
4k 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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1answer
323 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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128 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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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
1k 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 ...
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1answer
159 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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3k 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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524 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
884 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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39 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
74 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
184 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 ...
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437 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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368 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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411 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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730 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\...
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241 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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236 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
528 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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188 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 ...