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

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Under what circumstances will the log of a variable be normal, given that the variable is not normal

Let us say there is a variable that is not normally distributed. Under what circumstances will the natural logarithm of the variable be normally distributed? I have seen many articles and papers ...
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33 views

R - Same Density but different QQ-Plot?

I have data variable corresponding to quotation amount and I want to find which statistic law this variable follow if there is one. It seems that the ...
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Loss Size Index Function of A Lognormal Random Variable

I have this tutorial question and I've gone through the solutions, getting all but one line of working. I broke down the question to this point but I can't seem to get out the following. So Loss Size ...
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25 views

Numerically Solve for Parameters Characterizing Lognormal RV that's Truncated from Above

I am trying to numerically solve for parameters characterizing a lognormal distribution truncated from above with first moment = mean, second moment = ...
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14 views

How do I check whether my data fits exponential or lognormal or weibull using chi square and ks tests in R?

I'm a newbie to R language and I need to quickly find whether a set of data I have in a CSV file fits the three distributions Generalized exponential, log normal and Weibull. I need to test it using ...
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27 views

kernel density estimation of the log-normal distribution

I stumbled upon the following issue I cannot make sense of: When using default choices, the KDE for a log-normal sample (green) does not look like a density that integrates to 1, compare the true ...
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50 views

Distribution of geometric mean of normally distributed independent random variables [closed]

Suppose we have $X(i)$ for $i=1,...,n$ normally distributed independent random variables with the same known $\mu$ and $\sigma$ for all: $$X(i) \tilde{} N(\mu,\sigma)$$ Suppose that we take the ...
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25 views

Adding two distributions with proportional means and standard deviations

I need to know the mean $\mu_z$ and standard deviation $\sigma_z$ of a log normal distribution $Z(\mu_z,\sigma_z)$ which is the sum of two other log normal distributions--$X(\mu_x,\sigma_x)$ and ...
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30 views

log normal distributions

Here is my questions: X and Y are random variables that are lognormally distributed. G(Y) is some function of Y. What is the expectation value: < X * G(Y) > This is the expectation value of the ...
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17 views

ANOVA on a normally and a log-normally distributed variable: what to transform?

For an analysis of variance the residuals (but not the data?) have to be normally distributed. So, I have two variables, one is normally distributed, one is log-normally distributed, and their ...
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18 views

Composing a likelihood function for a convolved normal- and lognormal- dataset

I am trying to use some implementation of MLE to solve for the parameters of a mixed normal and lognormal population, and have had no end of trouble. A colleague and the internet has me convinced ...
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2answers
48 views

Log of Average v. Average of Log

I am constructing a dataset of monthly averages based on daily data. This dataset will be used for standard regression analysis. I anticipate wanting to transform the dependent variable, which has an ...
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1answer
26 views

Data analysis: how to compare 2 variables from each subject across 3 groups of 200 subjects?

New here and not a statistician, am MD doing research. Need advice on best method for data analysis. I have 3 groups of 200 subjects each. We collected 2 data points (A,B) from each subject. Baseline ...
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47 views

Not all positive-definite matrices are valid covariance matrices for lognormal variables

A simple method to generate correlated lognormal variables $X_i$ that obey a covariance matrix $C_{\mathrm{ln}}$ with elements $c_{\mathrm{ln}}^{ij}$ is to first compute the covariance matrix ...
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1answer
71 views

Interpreting test results on log-transformed data

I have data that is not normally distributed. I can log-transform it to be normally distributed, and then perform, for example, a t-test. But how do I interpret the results of the t-test? Do I have ...
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34 views

How to test whether part of the sample follows log-normal distribution?

I have a sample data that look like the following figure in a Q-Q plot with log-normal distribution. I performed an Shapiro normality test on the logarithm of the data, and reject the null hypothesis ...
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1answer
69 views

Weighting observations and measurement uncertainty in bayes

I am working on using MCMC (via STAN) to estimate model parameters for a bunch of observations with measurement uncertainty. I'm having problems with weighting each observation, and have reduced the ...
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13 views

How to reconstruct moments from aggregated data?

Let $X_{1\ldots n}$ be a stochastic variable that is log-normal distributed, with parameters $\mu$ and $\sigma$. Now suppose all $X_i$ are aggregated into $Y_{1\ldots m}$ where $Y_1$ is the mean of ...
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1answer
116 views

Can quantiles be calculated for lognormal distributions?

I just talked to someone who stated that quantiles cannot be computed for lognormal distributions. or it does not make sense. Is this true?
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51 views

Simulating lognormal data - not just log(mean) and log(sd)?

According to this question, to simulate a log-normal dataset with a mean and SD known, you just enter log(mean) and log(sd). For example, lets say I wanted a mean of 5 and SD of 2. ...
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134 views

Confidence Interval of a Lognormal Random Variable

Just learning some stats, so please forgive if this is simple but I couldn't find a good explanation. Let $X \sim \mathcal{N}(\mu,\sigma^2)$ and $Y = e^X$. To find an approximately 95% confidence ...
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1answer
33 views

Lognormal distribution using normal distribution inputs

I'm simulating lognormal data in R log(Y), using the mean and standard deviation of Y. This article outlines it very well! One step in the article I'm having trouble solving how it works though. ...
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How to calculate log-normal distribution parameters with partial data?

Imagine we have a partial data and we know that this partial data represent only the left 5% of the log-normal distribution, which the overall data follow. How can we calculate the mean-log and sd-log ...
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184 views

Lognormal Regression?

I'm trying to model a lognormal response variable. I want to take the log of the response variable and do a least-squares regression line over my predictive variable. However, I'm worried about ...
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15 views

estimating a survival function using a lognormal distribution

I am trying to fit multiple distributions to survival data. Now I am having some trouble with the lognormal distribution. I want to use the following formula: S(t)=1-Φ((log t-mu)/ σ My outputs from R ...
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fitting parametric survival curves on Kaplan Meier probabilities in aggregate data

Lets suppose I have aggregate survival probabilities (NOT individual level data) from Kaplan Meier curves. I would like to curve fit different "types" of distribution like exponential, weibull, ...
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69 views

Why are server response times distributed lognormally?

I found out that webserver response times are typically modeled as coming from a lognormal distribution here. What I don't quite get is why this is the case! In particular, Wikipedia states that a ...
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1answer
38 views

Correlation / clustering over lognormal data

I'm working with some financial data and it turns out my data is pretty much lognormal distributed. The question I have is, which produces "better" results: using plain data to find correlation / ...
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839 views

How to avoid log(0) term in regression

I have following simple X and Y vectors: > X [1] 1.000 0.063 0.031 0.012 0.005 0.000 > Y [1] 1.000 1.000 1.000 0.961 0.884 0.000 > > plot(X,Y) I ...
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Difference of two i.i.d. lognormal random variables

Let $X_1$ and $X_2$ be 2 i.i.d. r.v.'s where $\log(X_1),\log(X_2) \sim N(\mu,\sigma)$. I'd like to know the distribution for $X_1 - X_2$. The best I can do is to take the Taylor series of both and ...
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1answer
55 views

Can I make a linear congruential generator with a lognormal distribution?

One of my class tasks is to make a simulation. I've gathered the data and done distribution fitting to it and the result of the distribution is log-normal. I have the code to generate random numbers ...
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23 views

Name for phenomenon which causes bias in estimation of extreme percentiles of a distribution fitted to points with large error bars

I have a series of small numbers (say 25-45) of values which were generated, and each value has an uncertainty associated with it. I also have a theory that says these points are supposed to fit well ...
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33 views

Correction for Log normal distribution

Context: I have observed continuous data $\boldsymbol{O}$, for each observation $i$ I have an assumed known $\sigma_i$ for each observation I have an expected model value $E_i$. $E_i$ was produced ...
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How to derive the cdf of a lognormal distribution from its pdf

I'm trying to understand how to derive the cumulative distribution function for a lognormal distribution from its probability density function. I know that the pdf is: $$f(x) ...
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94 views

How to fit discrete data that have mode 0 to a log-normal distribution?

I am trying to figure out how to fit a log-normal distribution to discrete data that have mode 0, in particular, without first removing the zeros. For example, paper citation data are said to be ...
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1answer
74 views

Hypothesis testing- lognormal distribution

I have a conditional mean and standard error for a parameter log-normally distributed. I want to test whether the mean of the distribution is significantly different from an alternate estimate of ...
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20 views

The distribution of a product between a Lognormal and a Beta is …?

I have to random variables expressed as $1 \times 1000$ vectors. One of the vectors $B$ is Beta distributed while the other $L$ is lognormal distributed. Upon element-wise multiplication, I get vector ...
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48 views

Estimating the variance of a sum of predictions

I have $N$ plots that were used to estimate a relationship between three predictor variables, $X_1$, $X_2$, $X_3$, and an outcome, $Y$, using a generalized linear (lognormal) model. The resulting ...
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17 views

Find the mean of lognormal rv's with available variance and the sum of rv's

I have the sum of a bunch of random variables $S$, v = [1 1 2 2 3 3 4 ...]; S = sum(v); I know that vector $v$ is lognormally distributed, BUT I DON'T KNOW IT. ...
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71 views

How to describe a function of two normal distributed random variables

I consider the generic problem $W(X,Y)=-2\ln(\frac{(X-Y)^2}{2(X^2+Y^2)})$ where $X$ and $Y$ are normally distributed random variables Can I make any statements about the distribution of $W$?
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40 views

Regression against polynomials and log-linear predictors

I have a regression problem where one of the predictors has a very good fit as $Y \sim poly(X_1, 2)$. However, $Y$ is clearly log-linear against my second predictor $X_2$, so $ln(Y) \sim ln(X_2)$. ...
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236 views

How to estimate parameters of a log-normal distribution?

I am using income data from the Current Population Survey for a small undergrad economics paper. In economics, there is evidence that the income of 97%–99% of the population is distributed ...
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1answer
39 views

Gamma Distribution with Percentages

I am dealing with a set of data that appears to follow a gamma distribution or a lognormal distribution but the only issue is that the data set is in percentages and both of these distributions don't ...
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245 views

Percent change interpretation in log-transformed regression: Percent change from what?

I am dealing with a regression model where both the DV and IV are log-transformed. I have found this explanation of how to interpret the effects (both in the Cross-Validated hyperlink and in ...
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Continuous distribution for discrete population: Assessment?

We model Inflow and Outflow [people per day] by means of stochastic processes. We would like to assess to what extent the resulting continuous distributions acceptably model the discrete variables. ...
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1answer
44 views

Forming Location-Scale Family for Log-Normal

For the random variable X with a log-normal pdf $f(x)=\frac{1}{\sqrt{2*\pi}}x^{-1}e^{-.5*log(x)^2}$ I am trying to find a location-scale family $h(x)$ such that $h(x)$ has mean 0 and variance 1 Now ...
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Distribution of proportions relative to sum of random variables

Let $X_1,...,X_n$ be iid lognormally distributed variables and $X_{sum} = X_1+...+X_n$. What is the distribution of $\frac{X_k}{X_{sum}}$ for each $k$ in $1..n$? What are their density functions? ...
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1answer
119 views

Mixture of Gaussians on Log of Data

I am practicing Mixture of Gaussians and found the below dataset snoq, which is the precipitation amounts recorded at a US region, with ...
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29 views

Combining two data sets with different weightings, possibly Bayesian Updating?

I am a PhD student and I am currently looking at railway track degradation. As part of this I am finding linear fits of the track geometry recordings against time to give a degradation rate. The ...
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9 views

Finding significant values in my tree-like distributed data

i have a question about my data. Let me first describe what i know about it. I know that the number of data points I have is large (200-1000) I know each data point value is greater or equal to 0 I ...