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

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Is the multiple of a lognormally distributed variable also lognormally distributed?

If $X$ is distributed normally $N(\mu,\sigma^2)$ then the variable $Y = \exp(X)$ is lognormally distributed. If the variable $Y$ is multiplied by some constant $C$: $$D = CY$$ Is the variable $D$ ...
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Tail probability for heavy tailed distributions

For some data (where I have the mean and standard deviation) I currently estimate the probability of getting samples greater than some x by using the Q function; i....
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48 views

Lognormal Distribution & Probability

Lognormal Probability: 2 Part Question for a Newbie: 1.) Assume I have a vector that I suspect is already logNormal (I didn't transform it) and I want to get the mean and variance. From what I ...
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How to transform one PDF into another graphically?

To understand what I mean, let's use two well-known distributions: the normal and lognormal ones. From the dataset point of view, if you take normally-distributed data and take their exponential, you ...
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Why is the arithmetic mean smaller than the distribution mean in a log-normal distribution?

So, I have a random process generating log-normally distributed random variables $X$. Here is the corresponding probability density function: I wanted to estimate the distribution of a few moments ...
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Get covariance from conditional covariance for lognormal (and other) observations?

Consider lognormal random variables $X_1$ and $X_2$ with correlation coefficient $ρ$ and a partial observation sample of them of length N, the sample being partial because it only contains occurrences ...
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10 views

log percent change of univariate data

wondering if you can help me decide on the right metric to report. I am comparing multiple treatments, the measured variable is logarithmic so I take the log of my measurements and do ANOVA on the ...
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11 views

What are some of the more popular variable transformations and why/when are they used (to handle what types of distribution problems)?

Like the title states, I'm interested in learning about the more popular data transformation techniques. I know the internet is abound in this information, but I'd like to hear from those working ...
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64 views

Equivalent of a flipped lognormal distribution

What distribution could represent a "flipped" (skewed left) lognormal distribution? For ex: what name would you do to the distribution in the figure below? I fitted the histogram with a Beta ...
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30 views

Multivariate log-normal probabiltiy density function (PDF)

The Multivariate Gaussian pdf is given by $$(2\pi)^{-\frac{K}{2}} \det(\Sigma)^{-\frac{1}{2}} \exp({-\frac{1}{2}}(X-\mu)' \Sigma^{-1} (X-\mu)) $$ The wikipedia for multivariate Gaussians is here ...
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26 views

skewness and hypothesis testing (t-test and anova)

Some of my variables are heavily positive skewed (left skewed). With log transformation, some are closer to normal distribution, but some are still positively skewed, though not that bad before log ...
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439 views

Bias of moment estimator of lognormal distribution

I am doing some numerical experiment that consists in sampling a lognormal distribution $X\sim\mathcal{LN}(\mu, \sigma)$, and trying to estimate the moments $\mathbb{E}[X^n]$ by two methods: Looking ...
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78 views

Approximate Order Statistics for lognormal variables

Are there any known formulas that approximate the expected value of the maximum of $N$ i.i.d. lognormal random variables? I am looking for something similar to: Approximate order statistics for ...
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53 views

Expectation of two identical lognormal distributions

I would like to compute the conditional expectation (on an interval from $c$ to $\infty$) of the minimum of two log normal distributions. Denote $X_1$, $X_2 \sim LN(0, \sigma)$, the associated ...
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108 views

The product of two lognormal random variables

Let $X_1$ and $X_2$ be two normal random variables. Write $X_1\sim N(\mu_1, \sigma^2_1)$ and $X_2\sim N(\mu_2, \sigma^2_2)$, to fix ideas. Consider the corresponding log-normal random variables: $...
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81 views

What to do with data that are bimodal at two tails of the distribution?

I am in a weird position where I prespecified a plan to use linear regression to analyze my data, and stated I would use transformations to address any assumption violations. I'm pretty certain my ...
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39 views

Estimate new values from a sample

I'm looking for a way to demonstrate how many individuals (N) are required to reach a known (Y) value. More specifically: I have N DBH (diameter breast height) measurements. N is a sample from a ...
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25 views

Taking the derivative of the log-normal pdf

It is said that if $S_T$ is log-normal, then its pdf is given by $$ g(x) = \frac{1}{x\sigma\sqrt{T}} \phi(\zeta(x)) $$ where $$ \zeta(x) = \frac{\log(x/S_0) - (r - \sigma^2/2)T}{\sigma \sqrt{T}} $$ I'...
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R: Box-plot on log scale vs. log-transforming *then* creating box-plot: Don't get same result

In the boxplot() function in R, there exists the log = argument for specifying whether or not an axis should be on the log scale....
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57 views

How to calculate Mean and Standard deviation in Lognormal distribution where only P90 and P10 are known

I have P90 and P10 of a lognormal distribution. P90=142.56 and P10=3415; I need to estimate the mean and standard deviation of this lognormal distribution. I have done the following steps and then ...
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42 views

Hierarchical Bayesian model - issues with JAGS/BUGS switching between lognormal and normal

I'm trying to construct a hierarchical model using JAGS, but I'm running into issues converting between normal/lognormal distributions and the more I stare at my problem, the more confused I get. ...
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How do I fit a set of data that has a lower and upper bound to a lognormal distribution in R?

I have data only above 200,000 and up to 1,000,000, is there a simple R command that will permit me to fit a lognormal distribution to this data? Same for a pareto distribution?
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16 views

Comparison of Scale Parameters

I have several lognormal models, created from reliability data set and I was wondering if there is a way (like Tukey, Scheffe) to compare the scale parameters, to see if they share a common parameter. ...
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Cross correlation of gaussian signals with its mean signal gives non-gaussian distributed scores

The following is my question: I have signals that contains noise, they are of the following form see the figure below.. Then I take the mean signal of all these signals (identical in length and shape)....
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63 views

sample size to estimate mean of zero modified log normal variable

I would like to estimate the average value of a variable "A" in a population. I think only 5% of the population has a figure of A > 0, 95% has A = 0. Using a previous non random sample, I believe the ...
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What's the story behind the log-normal distribution?

I have been playing around with datasets for the past while for practice. I've noticed that a distribution that looks something like the following appears: This shape appears frequently! I can ...
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46 views

Jointly Sufficient Statistic Question

So here is a problem I have been working on: Suppose that survival time $X$ has a lognormal distribution with parameters $\mu$ and $\theta$ (which are the mean and standard deviation of $\log(X)$, not ...
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21 views

Generate Example data for which it is difficult to distinguish between Gamma, Weibull and log-normal fit using R?

I'm trying to generate a data set, as a demonstration case, to show a case in which it is difficult to distinguish between Gamma, Weibull and log-normal distribution. To do this I generate some data: ...
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20 views

Difference between gaussian and lognormal

I have to study tolerance intervals for a distribution of a random variable Z that is given by the difference of a normal X minus a (independent) lognormal Y. To begin with I tried to get an ...
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34 views

R timeseries data thats not normally distributed

I have time series data set in R that is skewed to the left, before I try and work with it should I be trying to "normalize" it IE x1ts is skewed x1tsNORM <- log(x1ts) will this make future ...
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When is it OK to write “we assumed a normal distribution” of an empirical measurement?

It is ingrained in the teaching of applied disciplines, such as medicine, that measurements of bio-medical quantities in the population follow a normal "bell curve." A Google search of the the string "...
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Why is this Bayesian estimate of a truncation-point so poor?

I have several datasets. Each dataset holds the masses of objects that have been subject to physical wear, expressed as a proportion of their original mass ($w$), and the amount of time that the ...
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zipf and correlated lognormal

I have been struggling with this for a while. I want to generate two random variables $X$ and $Y$ with a particular correlation $\rho$ where $X$ is the file popularity (zipf distribution) and $Y$ is ...
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58 views

Skewness of log-normal distribution only depending on variance?

Wikipedia says that the skewness of the log-normal distribution only depends on the variance of the underlying normal distribution. Skewness: However, from my point of view the skewness increases ...
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Interpreting Standard Deviation of Natural Log Transformed Data

I am interested in interpreting (back transforming) the effect of a one standard deviation (sd) increase in a log transformed on the non-transformed variable. So let's say I have a variable Y: ...
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Under which conditions two lognormal distributions l1, l2 have median(l1+l2) = median(l1)+median(l2)?

are there any conditions on two lognormal l1 and l2 RVs which satisfy: median(l1+l2) = median(l1) + median(l2) They can be correlated and/ or dependent. In case the answer is affirmative, is it ...
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Transformation of data with zero and R squared

I have a conceptual concern about data tranformation and R^2. Often we transform data to respect the assumption of the linear model. Therefore, we can use multiple type of transformation such as log ...
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1answer
57 views

lognormal distribution average and variance

I am trying to get acquainted with this type of distribution, and part of it is exploring what random number generation with scipy.stats produces. I have noticed ...
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30 views

Expected value log-normal variable

Suppose $X_t$ and $Y_t$ are bivariance have standard normal distributions with mean zero and variance 1. The covariance of $X_t$ and $Y_t$ is $Cov_t(X_t, Y_t) = c$, where $c$ is a constant. What is ...
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How should I transform a featureset (15000 variables) that is mostly presence/absence, but present values are lognormal distributed?

I am trying to learn machine learning and have a nice featureset with a binary classification. The dataset is 15000 variables and 2500 data rows. For every data row, almost all variables are 0, and ...
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179 views

What is the distribution of $e=Y-\mathbb{E}(Y)$ where $Y=\exp(u), \ \ \ u\sim\mathbb{N}\left(\mu,\sigma^2\right)$

As $Y$ is log-normal we've $Y\sim \mathbb{LN}\big(\exp(\mu+\sigma^2/2),\exp(2\mu+\sigma)(\exp(\mu^2)-1)\big)$. Now I define $e = Y - \mathbb{E}(Y) = Y - \exp(\mu+\sigma^2/2)$. As $e$ is the ...
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127 views

Negative variance in a log normal distribution

I'm currently trying to solve a maximum likelihood estimation of a random variable which is assumed to be log normal distributed. For this I compute the log of all sample values I have in order to ...
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1answer
53 views

log hazard function in R

I'm trying to write out the log hazard function of the lognormal distribution and use this in R. Using the survival function: and the hazard function: I have the following for the log(hazard): ...
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78 views

How do I determine parameters of normal & lognormal distribution given two points?

Assume I have two values which represent two quantiles for the same lognormal and/or normal distribution. How can I determine the parameters of the distribution? ...
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Calculating actual quantile from poorly defined lognormal distributions

I have a dataset in which the uncertainties in various parameters are modelled with a lognormal distribution. After the experiment I get a single number result. As part of a lookback to understand how ...
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137 views

How to interpret confidence intervals from R t.test when log transforming the data

I have a quite large dataset that contains the time it took to make two different types of requests over a network. I would like to calculate how big the difference between the two types are. I was ...
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lognormal with very large mean, but small sample value

Let $X \sim N(\mu, \sigma^2)$, where $\mu = -800$ and $\sigma = 76$ Let $Y = \exp(X)$, so Y has a lognormal distribution, $E(Y) = \exp(\mu + \sigma^2/2) = \exp(2088)$, which is a very large number. ...
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72 views

Name for exp(log normal) distribution

If the log of a dataset fits a normal distribution, then the data is said to be log normal. If the log of a dataset fits a log normal distribution, is the data said to be log log normal? Is there a ...
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154 views

Transformation from Normal to LogNormal in R

I need to generate random numbers from LogNormal distribution by using transformation with Normal. Although I tried some way, it didn't work. How can I make it ?
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Taylor Expansion of Power of Cumulative Log Normal Distribution Function - Show Lagrange Remainder tends to Zero

QUESTION I am looking to find a simplification of the expression below. I have attempted this using the Taylor series. The question then remains if we can show the Lagrange remainder goes to zero. I ...