Questions tagged [lognormal]

A lognormal distribution is the distribution of a random variable whose logarithm has a normal distribution.

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Comparing Discrete Lognormal Distributions

Is it possible to have the following: Create an approximation of the discrete lognormal distribution? Given a discrete distribution in the form of a histogram, is it possible to compare its ...
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Let 𝑋 be a Log-Normally distributed RV with 𝜇 = 3 and 𝜎 = 2. Determine 𝐸[max(𝑋 − 100, 0)]

See the question above. I am not quite sure, if my result is correct, because I do not have any solutions. I tried with the following formula: $$ E[X] = e^{\mu+\frac{1}{2} \sigma^{2}} \cdot \Phi\left(...
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Let 𝑋 be a Log-Normally distributed RV with 𝜇 = 3 and 𝜎 = 2. Determine 𝑃 (100 ≤ 𝑋 ≤ 150)

I do not get how $\Phi\left(\frac{\ln (100)-3}{2}\right)$ and $\Phi\left(\frac{\ln (150)-3}{2}\right)$ should give me the probabilities 0.7889 and 0.8426 respectively. I looked at the distribution ...
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How to interpret a Log Normal Distribution

I have a dataset with 3 columns that are found out to be log-normally distributed. I am a little bit confused about how can I draw the conclusion in a log-normal distribution similar to Normal ...
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Should I use log transformed pharmacokinetic data or use GLM gamma regression with log link?

I was taught, that when we deal with data of multiplicative nature, following the log-normal distribution, like in pharmacokinetic analyses, we should log the data first to enable classic parametric ...
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Appropriate to fit lognormal model to data with heavy tail?

I am attempting to standardize recreational fishery CPUE data. I am using a delta approach, with a binomial model fit to the presence/absence data and a lognormal model fit to the positive ...
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What is the full-conditional distribution for $log(\sigma) \sim N(\mu_\sigma,\tau_\sigma^2)$?

What is the full-conditional distribution for $[\sigma|\textbf{y},\mu]$ given the following hierarchical structure?: $y_i \sim N(\mu,\sigma^2)$ $\mu \sim N(\mu_0, \sigma^2_0)$ $log(\sigma) \sim N(\...
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How to derive CDF of lognormal distribution? [duplicate]

Can someone explain how I can derive CDF for lognormal distribution from this PDF: $$f(t)=\frac1{\sqrt{2\pi}}\gamma t^{-1}e^{-\gamma^2(\log(\lambda t))^2/2}$$ I need this CDF function for Survival ...
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How is that possible that simple arithmetic mean works well even for strongly skewed distribution?

I was taught, that the arithmetic mean is sensitive to outliers and skewness. This was natural to me - the observations lying far from the "central point" of the distribution "pull" the measure ...
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Why summarise right-skewed distributed (log-normal) data with geometric mean rather than its expected value?

I am very confused. The first raw moment calculated from sample, the arithmetic mean, is the BLUE estimator of its expected value. So there is no better one. At the same time, I was told that the ...
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Deriving the un-normalized log posterior on sigma

Hello I'm trying to derive the un-normalized log posterior on sigma this is what I have so far $$ p \left(\sigma \mid \mathbf{x}, \mu\right) \propto \log \left( p \left(\sigma \mid \mathbf{x}, \mu\...
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Question about the decision between normal and lognormal distribution in a linear model

I hope someone could help me with the following problem: If I create a linear model that predicts the height of people (y) with the following parameters: y = a + b*(xi-xavg) with "a" the normally ...
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Sum of dependant log-normal distributions with large uncertainties

I need to sum many lognormal distributions, which are correlated among them. My distributions simulate vary uncertain gas emissions. I know their mean value, the percentage uncertainty (defining the ...
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QQ plot distribution check

I want to check if a distribution is log normal or not by using qq plot. So for convenience I am creating a lognormal distribution using stats and checking it in ...
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In the case of lognormal distribution, when can the median be more efficiently estimated than the mean?

I understand, that in the case of normal distribution, the estimation of the mean (from samples) is more efficient (i.e. of less risk), than the estimation of the median. According e.g. to this post, ...
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Predicting y from log y as the dependent variable

In the book Introductory Econometrics by Wooldridge the chapter, which deals with predicting values of $\hat{y}$ (chapter 6.4 in the 5th edition) states the following: If the estimated model is: ...
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Determining The Underlying Parameters In Lognormal Distribution

I have the following problem: " Let $ \epsilon $ be a normal random variable with variance $ \sigma^{2} $ and mean $ \sigma^{2}/2$. Then $\phi \equiv e^{\epsilon}$ is a lognormal random variable, $\...
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Transformation of a variable

Suppose I have a stochastic variable $X,$ that is not normally distributed using Shapiro Wilk test. Than I transform the variable using log transformation, and now the log transformation is normally ...
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Generate Multivariate Log-Normal Variables with given Covariance and Mean

Let ${\bf X}=(X_1,...,X_n)$ be an $n$-dimensional log-normal random variable. I want to $force$ my random variables to be such that $Cov(X_i,X_j)=\Sigma_{i,j}$ and $E(X_i)=\mu_i$ where $\Sigma_{i,j}$ ...
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How to estimate log-normal distribution parameters from a set of data?

I don't have any background in statistics, so maybe I may say things that are incorrect. I have to model the production of waste deposition at each container of a set of containers and I have access ...
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Get log-normal distribution parameters by min, max, mean

Assuming there are three values existing for a dataset, min=100, mean=1000, max=10000. Is it possible to derive the mu and sigma value of assuming the data fit to lognormal distribution? And if yes, ...
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Log-normal variance estimation

I have generated some log-normal sample data with python (I tried also with Wolfram Mathematica). Let's say with parameters $\mu = -14.6$ and $\sigma = 3.6$, but even with other parameters I observe ...
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Is there a closed-form expression for the Poisson Lognormal pmf?

Suppose the $\lambda$ parameter of a Poisson distribution is generated from a $LogNormal(\mu, \sigma)$ distribution. Can the final pmf be expressed with only elementary functions? $$f(x;\mu,\sigma)=\...
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From log.normal to normal [duplicate]

I have the following issue. With a Monte Carlo simulation I have generated a data set, x values and their frequencies. When I plot the histogram I noticed that the shape of the distribution is skewed....
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Can distributions that are in the exponential family, but not the natural exponential family, be formed as GLM?

The lognormal and beta distributions are in the exponential family but not the natural exponential family. Generalized Linear Models are often advertised as being models for response variables that ...
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Strange connection between Bernouilli, Uniform and Geometric distributions

Final update on 11/29/2019: I have worked on this a bit more, and wrote an article summarizing all the main findings. You can read it here. Let us consider $Z = X_1 + X_1 X_2 + X_1 X_2 X_3 +\cdots$ ...
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Positive sums of small quantities at low resolution

Many measured continuous quantities are in fact sums of discrete events measured with insufficient resolution (e.g. electric current) and thus conveniently modeled by continuous probability ...
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Distribution for strictly positive variables

What are equivalents of the normal distribution when working with strictly positive quantities? That is the distributions that are: 1. Mathematically convenient to work with 2. The random variable ...
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Correlation between log normal variables and a normal variable

I have a variable $z$ given by: $z=\sum_{i=1}^n z_i$ where $z_i$ are random variables with $z_i \sim N\left(0,1\right)$. Then it will be $z \sim N(0,n)$ and the correlation between a variable $z_i$ ...
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The product of 3 lognormals coming from tri-variate normal distribution [duplicate]

My question is similar to this one The product of two lognormal random variables, but I'd like to do it with three lognormals. The referenced question cannot be applied twice since the correlation ...
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If $X$ has a log-normal distribution, what is the distribution of $Y=\exp X$?

I'm just looking for the name of this distribution, assuming it has a name. I call it the log-log normal distribution, for lack of a better term. It's support domain is $[1, \infty]$.
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Multivariate Bayesian Car Model Result

I have developed a multivariate Bayesian Car model for three crash severity level analysis. I found that the covariance for both heterogenous effects and the spatial effect is not significant for any ...
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For lognormal distribution which one is preferred? Log 10 or Ln or Log 2?

I want to perform a linear regression analysis. The distributions of data for all continuous variables are not normal. The tail of graph is to the right and thre highest point of graph is due to the ...
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Convert median absolute deviation (MAD) to SD for log-normal distribution

How do I convert the $\text{MAD}$ (median absolute deviation from the median) of data that is drawn from a log-normal distribution to the standard deviation of a log-normal distribution? To clarify, ...
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Estimating parameters for the product of a lognormal random variable and a uniform r.v

Suppose I have a random variable which I suspect is the product of a lognormally distributed random variable $X$ and an independent uniformly distributed variable $U(0, 1)$. (The variables are the ...
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Lognormal standardisation

Suppose we have a standardized normal $Z_1 \sim \mathcal{N}(0,1)$, and take the associated lognormal $X = e^{Z_1}$. Suppose that with have a non-standardized normal $Z_2 \sim \mathcal{N}(\mu,\sigma^2)...
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Need advice on acceptable means to convert lower and upper confidence limits of a lognormal distributions to median and geometric standard deviation

I have offered to help convert a monte carlo simulation from guesstimate (a streamlined monte carlo simulation tool) https://www.getguesstimate.com/ to Analytica in order to perform a more in depth ...
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Log level model - do I exponentiate all coefficients for interpretation?

I'm working with a regression model where I have a log transformed target variable due to the distribution of the log transformation being more normal. I have some numeric variables and also some ...
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Can someone explain to me the parameters of a lognormal distribution?

I'm doing some reading and this is the definition I got from DeGroot's book: Does that mean the parameters are the same? For example, assume X is lognormally distributed and Y is normally ...
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How to find an expression of the variance of a Poisson-Lognormal distribution?

I am using a model for the number of goods in a supermarket cart with a Poisson-lognormal distribution (a lognormal mixture of Poissons). I would like to find an expression of the variance of this ...
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How reliable is a linear model on log-transformed data

I have collected timing data in which the residuals are non-normally distributed. I log-transformed the data, and then conducted a linear mixed-model regression analysis. (The residuals from the log-...
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Weird sample variance when creating a lognromal sample with pre-defined mean and variance [duplicate]

I have been working with lognormal distributions as a proposal distribution for some MCMC routines which require the proposal distribution to have some pre-defined sample mean and variance, $m$ and $v$...
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668 views

generalized linear model with log link using log transformed fixed/random effects?

I am modelling a longitudinal dataset consisting of a continuous response variable (mutation count) with a binary predictor (medical history, ie previous medications) while accounting for time and ...
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log transformation for geom_histogram and stat_function

I am playing around with lognormally distributed data, and I would like to visualize it both on the original and log scale with ggplot ...
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Interprete GLMM Estimates with log link

i am relatively new to this field and this is my first time using Generalized Linear Mixed-Effects Model. my response variable is Reaction Time (RT) and i have two fixed effects: prime and type. both ...
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If two lognormal distributions have correlation $\rho$, what is the correlation between the log of those distributions?

Suppose I have $X,Y$ which are lognormal with correlation, $\rho$, what is the correlation between $log(X)$ and $log(Y)$? I tried working it out analytically and I'm getting that you have to ...
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Variance of X and Variance of Log(X). How to relate them?

I have the variance of a random variable X and I want to obtain the variance of log(X). Is it possible if I dont know its PDF? If I assume that X has a lognormal PDF, how variances should be related?
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Mean of a Poisson-Lognormal Distribution (PLN)

I would like to calculate the mean value of a PLN distribution, $$ f(x;\mu,\sigma)=\frac{1}{x!\sigma\sqrt{2\pi}}\int_{0}^{\infty}\lambda_\ast^{x-1} e^{-\lambda_\ast} e^{-\frac{(log(\lambda_\ast-\mu)^2}...
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Conditional distribution of a function of a random vector given conditional distribution of random vector

Let $\mathbf{X}=(X_1,...,X_n)^T$ be a multivariate normal distribution. Now we have $\mathbf{Y}=(Y_1,...,Y_n)^T$ defined by $Y_i = e^{X_i}$. Let $\mathbf{Y^1}, \mathbf{Y^2}$ be partitions of $\mathbf{...
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Why Does a Monotonic Transformation Of Dependent Variable Change Variance Explained In Random Forest

I am working with the Boston data set in R. I have read that random forest should be able to deal with untransformed data. In my example I do a log transformation of the dependent variable. My ...

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