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

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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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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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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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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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21 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 $$ \zeta(x) = \frac{\log(x/S_0) - (r - \sigma^2/2)T}{\sigma \sqrt{T}} $$ ...
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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 ...
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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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28 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 ...
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42 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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63 views

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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38 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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1answer
19 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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18 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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31 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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75 views

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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42 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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45 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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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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178 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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109 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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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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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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41 views

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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1answer
104 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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106 views

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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65 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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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 ...
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Is there any paper about the distribution of difference of log-normal variable?

I am working on the problem relating to the difference of log-normal distribution. I have found several papers about this topic, however, none of them gives me the answer I want. More specifically, ...
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Log Transformations and Z-Scores

I have some skewed variables in my dataset, I did log-transformations to make them more normal. Do I now turn them into z-scores if I am running analysis with other standardized variables in my ...
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153 views

Approximating $\log( E(X))$

I was casually reading an article (in economics) which had the following approximation for $\log(E(X))$: $\log(E(X)) \approx E(\log(X))+0.5 \mathrm{var}(\log(X))$, which the author says is exact if ...
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How to pre-process data for partial least square PLS regression in R?

I have a data frame that is consisted of 20 observations and 35 variables. I want to prepare the data for partial least square regression PLS in R. Many authors suggest: 1)Check whether the ...
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1answer
101 views

Goodness of fitting: power-law or discrete log-normal?

I'm not a statistician, so I would be grateful if someone can help me with my questions. I have a dataset of users' check-ins of a social network. I'm verifying if these data are distributed ...
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1answer
68 views

Variance for arbitrary power of log normal variate

Say we have a R.V. called $X$ and let $\ln{X} \sim N(\mu, \sigma^2)$, therefore $X$ follows a Log Normal distribution. Then let another R.V. $Y = X^{\gamma}$, where $\gamma$ is just a constant. Does ...
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304 views

Can I get the parameters of a lognormal distribution from the sample mean & median?

I have the mean and median values for a sample drawn from a lognormal distribution. Note that this is not the mean and median of the logs of the variable, though I can of course calculate the logs of ...
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Conditional expected value for dependent Log-normal Distribution

I'm trying to find the expected value of a FX derivative which is log normally distributed, dependent on another derivative, but do not have the direct co relation between them. Instead I'm given the ...
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765 views

Calculate variance and standard deviation for Log Normal Distribution

I am trying to calculate the variance and standard deviation for a log normal distribution. I was able to calculate the mean after reading this stack exchange article How to calculate a mean and ...
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1answer
63 views

Quantify Difference/Distance between Lognormal distributions

I am trying to determine a metric that quantifies the distance between two continuous lognormal distributions. The data is actually a mixture of two lognormal distributions (I am not sure if this can ...
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1answer
72 views

How to find expected value for this financial expression

I am reading a research paper, and there is such condition: $$ E_t\Big[\frac{(F_t - S_{t+1})P_t}{S_tP_{t+1}}X\Big]=0 $$ where $E_t$ is expected value. I suspect that $E_t[F_t] = F_t$ because this ...
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Fitting datas, lognormal and beta distribution, interpretations

I've been given some data that should come from a lognormal distribution. I've got some issues concerning the fitting, here's what I did. ...