Questions tagged [inverse-gaussian-distrib]
A right skew continuous probability distribution on positive real numbers.
33
questions
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25 views
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?
...
1
vote
0answers
23 views
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 ...
2
votes
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 ...
6
votes
1answer
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 \...
1
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0answers
25 views
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:
...
3
votes
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 ...
2
votes
0answers
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 ...
2
votes
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}{...
18
votes
2answers
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 ...
0
votes
0answers
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 ...
0
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0answers
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 ...
3
votes
0answers
42 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 ...
0
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0answers
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 ...
14
votes
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 ...
4
votes
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 = ...
1
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0answers
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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0answers
1k 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 ...
2
votes
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 ...
3
votes
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, ...
1
vote
2answers
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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0answers
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 ...
1
vote
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 ...
1
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0answers
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 ...
1
vote
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, $...
3
votes
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 ...
3
votes
0answers
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 ...
2
votes
0answers
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-...
1
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0answers
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{...
0
votes
0answers
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\...
3
votes
0answers
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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0answers
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 ...
2
votes
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 ...
1
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0answers
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 ...
