Questions tagged [inverse-gaussian-distribution]
A right skew continuous probability distribution on positive real numbers.
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Closed-Form Lambda for Yeo-Johnson-Transformed Normal-Inverse-Gaussian-Distributed Random Variables
I would like to know whether there exists a closed-form solution for the $\lambda$-parameter that maximizes the log-likelihood function of Yeo-Johnson transformed random variables that (before the ...
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How do I appropriately code a gamm() model with an inverse.gaussian family and autocorrelation structure?
I am incredibly new to generalized additive modeling, so I apologize in advance for any and all naiveté. But I believe GAMMs are the appropriate methodology for my data. I am working with fish ...
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Properties of the inverse normal cdf and permutation probabilities as models for horse racing
Let $T_i$ be the running time of horse $i$ and $T_i \sim N(\theta_i,1)$ and the $T_i$'s are independent. Then Henery (1981) showed that the probability $P(T_1<T_2<\cdots <T_n)$ can be ...
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Adequate sample size for non-normal population
There are 197,058 record holders (population) with an average of K shares each. I don’t know K, and the sample collected so far of ~24,000 observations appear to be non-normal (inverse gauss). I’m ...
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How to interpret beta coefficients of a generalized linear model using inverse gaussian
I made a generalized linear model with an inverse gaussian link.
...
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The mean of Gaussian distribution subject to another Gaussian distribution, how to derive it？
I got a fomula
$$N(y;cx,R)N(x;\bar{x},\Sigma)=N(y;c\bar{x},S)N(x;g,F)$$
where:
\begin{align}S&=c\Sigma c^T+R\\g &=\bar{x}+\Sigma c^Ts^{-1}(y-c\bar{x})\\F &= \Sigma - \Sigma c^T s^{-1} c \...
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The probability/cumulative density function for inequality of two random variables
I have two random variables X and Y which came from different inverse gaussian (IG) ...
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Relationship between standard normal distribution and normal distribution
Assume we have $X\sim \mathcal{N}(\mu,\sigma^2)$. What is the value/formula of
$$\Phi^{-1}(\Phi_{\mu, \sigma}(x)),$$
for any $x\in \mathbb{R}$?
$\Phi^{-1}$ denotes the inverse of the standard normal ...
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Confused about inverse function (quantile function)
I read a post that says:
"Math definition is that the quantile function is the inverse of the distribution function at α. It specifies the value of the random variable such that the probability ...
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Generalized mixed-effect regression model (GLMM) with negative reaction times as a result of baseline RT subtraction
I am hoping to get some advice for examining differences in reaction times (repeated sampling) as a measure of cognitive load between groups.
Dataset: The response variable I am using is reaction ...
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I'm getting confused with Gaussian Process Prior sampling
I'm having a hard time understanding Gaussian Processes prior sampling. Here is the article from medium I'm using to learn about Gaussian Processes Article link.
I'm going to start off by explaining ...
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Gamma family as conjugate prior of Inverse Gaussian with known $\mu$
I want to show that, when $\mu=\mu_0$, then gamma family $\Gamma(a,b)$ is a conjugate prior to inverse Gaussian with density $f(x,\mu,\lambda)=\sqrt{\frac{\lambda}{2\pi x^2}}exp[-\frac{\lambda(x-\mu)^...
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qqplot of inverse Gaussian distribution in r
I wanted to draw a qqline of my data with the inverse Gaussian distribution, however, the line printed does not seem to be right, for details see the picture attached.
someone help me please
thanks
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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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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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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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Creating values from a normal inverse gaussian (NIG) distribution
I have a vector of empirical observations 'a' containing about 16000 values.
empirical data
The empirical histogram looks like the following:
I'm trying to test, whether the normal inverse gaussian (...
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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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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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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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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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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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inverse gaussian glm residual deviance
I am currently modelling crash severity data with an inverse gaussian glm with a log link. I read that
model residual deviance ~ $\chi^2_{n-p}$
Would there be an obvious reason why the residual ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...
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