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

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How to convert parameters of a multivariate lognormal to a multivariate normal

I have the means and the variance-covariance matrix of a multivariate lognormal distribution. How to use them to obtain the means and variance-covariance matrix of the corresponding multivariate ...
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Sampling under assumption of log normal distributed data with sample mean and standard deviation

I have the sample mean and the sample standard deviation of income calculated from individual tax data of all citizens in country (let's call this data X). I do not have access to this tax income ...
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23 views

Estimate time from interval-censored data with bayesian approach

I have interval censored data for incubation period and I suppose that the exact time Ti is included in each interval of the data [L;U] and follows a lognormal distribution (mu,sigma2). I would like ...
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61 views

How to find normal and lognormal moments, given partial information?

$Y=\ln(X)$. $X$ is lognormal and $Y$ is normal. If all I know is the arithmetic mean of $Y$ and the standard deviation of $X$. What is the formula to calculate the arithmetic mean of $X$ and the ...
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Interpretation of log transformed predictor in negative binomial regression

I mainly want to make sure that I'm making the correct interpretation here. I built a negative binomial regression model predicting a count variable. There was evidence of overdispersion or I would ...
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11 views

Plotting raw data, but running statistics on log-transformed data

My data is non-normal, I want to show my raw data, in a scientific journal, by median +/- mad, to show the true nature of the data. However, if log-transformed, the data is normal. Can I then ...
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25 views

On log-normal distributions

Since my research data seems to follow log-normal distribution, I was curious to learn more about the topic. In addition to very nice answers here on Cross Validated (In linear regression, when is it ...
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1answer
23 views

convert lognormal Cumulative Density Function P90 and P10 values to mean and sigma [duplicate]

Practioners are used to defining lognormal distributions in terms of P90 and P10 cumulative density function values. To utilize these esperts' input I need to be able to convert these P90/P10 values ...
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40 views

R: random sampling for multivariate normal and log-normal distributions

I want to generate random monthly (m) temperature (T) and Precipitation (P) data considering that both variables are intercorrelated (rTP[m]) The tricky thing is that my random variables that have ...
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24 views

Terminology and handling of log-normal mixture distributions

The definition of a log-normal distribution of a random variable is based on normality of its logarithm. I'm curious whether there exist a specific term for cases, where log-transformed data does not ...
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1answer
36 views

Summarizing a lognormal distribution with geometric mean and standard deviation

I have some data that I strongly suspect are lognormally distributed, and I'd like to summarize the distribution using the mean and standard deviation. I've read that with lognormal distributions the ...
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1answer
36 views

Multiplicative error and additive error for generalized linear model

If the following generalized linear model was used, how should I interpret the error term? link function: natural log distribution: Gamma distribution i.e., $\ln E(Y)=X\beta$ and $E(Y)=\exp(X\beta)$ ...
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Common name for distributions that are bounded on one side

Is there a common name to refer to distributions that are bounded on one side, and unbounded on the other side? For example, log-normal distribution, where the minimum value is zero, the maximum is ...
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59 views

Boxplots with lognormally distributed data

Context Environmental data (e.g., pollutant concentrations in water, soil, air) are often lognormally distributed. Even when they are not, we tend to assume that they are (for better or worse). ...
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25 views

Proper back-transformation of lognormal standard deviation to find confidence intervals around a mean [duplicate]

I want to determine the 95% confidence interval of a mean. I logged-transformed my data in order to achieve a normal distribution. Several observations contained 0, so I changed these to 1 so that ...
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3answers
122 views

Estimating the ratio of cell means in ANOVA under lognormal assumption

I am conducting a two-sample test (1-way ANOVA with 2 treatments), and the goal is to estimate the ratio of cell means assuming that the data are lognormal. A simple approach is to log the response ...
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1answer
76 views

Sampling from a lognormal distribution

Suppose we are given $\mu$ and $\sigma$ for a lognormal distribution with random variable $X$. $\mu$ is the mean of the variable's logarithm and $\sigma$ is the standard deviation of the variable's ...
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21 views

How to get the values for the graph of confidence limit for the exceedance fraction vs z-value?

I am working on an application for a team of industrial hygienists and I need to create a lookup function for the confidence limit for the exceedance fraction. I found what I need from this book: ...
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85 views

$E[e^{cX}]$ where $c < 0$ and $X$ is lognormally distributed

I am trying to calculate the expectation $$E[e^{cX}]$$ for arbitrary $c<0$ (for $c>0$ the expectation is infinite) if $X$ is lognormally distributed, i.e. $\log(X) \sim N(\mu, \sigma)$. My idea ...
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48 views

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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75 views

Sum of lognormal distributions

I am to find the expected value, variance and, preferably, the distribution of the variable $z_n$, where $z_n$ is given by \begin{equation} z_n = \exp\left\{ \Delta t \sum_{i = 1}^n k_i ...
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2answers
103 views

Prediction interval for a fitted log-normal distribution

What I am trying to do is to fit a log-normal distribution to a data-set, and then determine confidence and prediction intervals for the fitted distribution - not just for the mean and sd estimates. ...
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1answer
64 views

Lower and Upper confidence limit on estimated arithmetic mean using Land's exact

I have to compute the LCL95% and UCL95% using Land's "exact" method. I computed the LCL and UCL for this lognormal distribution using another technique and I cant find anything for Land's Exact ...
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38 views

Expectation of the product of two log normal variables

I am struggling with a proof, and I am wondering if anyone can help or point me to the right direction. Suppose that we have two variables, $X$ and $Y$, and they follow a multivariate normal ...
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1answer
27 views

create bins for lognormal data for cluster analysis

I have a series of dollar amounts that are highly right skewed, but are roughly log-normal. i want to put this grouped dollar amount as a predictor variable into a latent class cluster analysis. In ...
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Extreme Value Theory: Lognormal GEV parameters

Lognormal distribution belongs to the Gumbel maximum domain of attraction, where: $F^{logN}(x; \mu,\sigma)=\Phi\left(\frac{\ln x - \mu}{\sigma}\right)$, $F^{Gum}(x;\mu,\beta) = ...
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203 views

How to calculate Estimated Arithmetic Mean for a lognormal distribution

I have been tasked to program functions from some Excel sheet into a asp.net app so it can be shared to my colleagues via a web interface. However, I am stuck on one thing. I have a set of variables ...
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28 views

Should I log transform my volatility variable?

I'm wondering if my volatility factor is specified correctly. My data consists of log returns on the S&P 500 index, a measure of news sentiment, and a newscount variable (# of articles published ...
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43 views

Match Right Skewed Distribution to Normal

I am running a simulation. One of my parameters is sampled from a normal distribution. I would like to perform a sensitivity analysis using a right skewed distribution. This is what I had hoped to ...
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86 views

Bayesian model with unknown mean and variance with lognormal prior

For $i=1, \ldots, K$ and $j=1, \ldots,n$, assume the following model. \begin{align} X_{ij} \mid \mu_i, \sigma^2 & \stackrel{_\text{iid}}{\sim} N(\mu_i, \sigma^2) \nonumber \\ \mu_i & ...
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1answer
40 views

Simplex Random Walk Mean

Hi I have two questions related to a previous question I asked here: Simplex Random Walk In this link it describes how to perform a random walk on the simplex. ...
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32 views

“Average” line over irregular log series data

I have simulation data from 1000 runs, plotting some measurable (in this case convergence of the algorithm) as a function of simulation time. Each run produces a discrete set of points ...
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48 views

Lognormal posterior?

If I have a relationship: $ y_t = a + \theta b_t \epsilon_t,$ where I observe $y_t$ and $b_t$. $a$ is a known parameter, $\theta$ is an unknown parameter with prior distribution at time $t$: $\theta ...
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37 views

Gibbs sampling with Log-Normal observations

I am writing a Gibbs sampler for data that is Log-Normal (LN) distributed, with unknown mean and variance. There is a wealth of information on inference for LN models when either the mean or variance ...
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96 views

parameter estimation of a mixture distribution

I have this mixture distribution $f(x) =w \cdot \mathcal{LN}(\mu_1,\sigma) + (1-w)\cdot \mathcal{LN}(\mu_2,\sigma) $ where $\mathcal{LN}(\mu,\sigma)$ is a lognormal distribution. I now have $j$ ...
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33 views

Decomposing a Combination of Distributions?

Let's say I'm studying the distribution/log-distribution of a random variable that may actually be the result of a combination of distributions. What are the ways I can check for this and possibly ...
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1answer
47 views

Why do the normal and log-normal density functions differ by a factor?

If a random variable $W$ is Normally distributed, then $\exp(W)$ is Log-Normally distributed. However, the pdfs of these two random variables differ by a factor of $\exp(W)^{-1}$. The Normal pdf ...
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1answer
197 views

Difference between log-normal distribution and logging variables, fitting normal

Context: I have a set of data that is bimodal, so I used the mixtools package in R to fit a bimodal normal distribution to it. It looked as if the normal did not fit very well, and given other similar ...
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1answer
76 views

Compare Log-Normal Distributions

I am looking at distributions for the fuel consumption of vehicles in the US and I have two sets of data: Data Set 1 - This is a dataset for the fuel consumption of all vehicles made available for ...
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50 views

Price levels and inflation in regressions

How would we include price levels in a regression? Would we just take the log of the price index number, e.g.: Consumer Price Index number provided by the Office of National Statistics (UK statistical ...
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1answer
34 views

Regressing a ratio on a component of the ratio

Is there anything wrong with regressing a ratio on itself? For example can we regress the log(savings ratio) on log(income) or the log(debt to income) ratio on log(income)? If not, should we use the ...
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1answer
36 views

product of normal and lognormal variates

If x and y are uncorrelated normal variates, x*exp(y) will have a symmetric unimodal distribution with positive excess kurtosis. Has this distribution been named and studied?
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161 views

If $X$ is lognormally distributed, what is the distribution of $1 / (1 + X)$?

Let $X$ be lognormal with parameters $\mu$ and $\sigma$ (such that $\log(X)$ is Gaussian with mean $\mu$ and variance $\sigma^2$). What is the distribution of $1 / (X + 1)$? I am wondering whether it ...
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1answer
124 views

How to calculate log-normal parameters using the mean and std of the given distribution

I have the mean (u) and the standard deviation (sd) of a continuous distribution (X). How do I solve for the mean (u_log) and standard deviation (sd_log) of the log of that continuous distribution ...
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34 views

How to compare two implementations of web service by parameters of distributions of their response times?

We are migrating web services to new platform. Current WS will be wrapped behind new platform's layer. We would like to define criteria for response times of wrapped WS that should be met so we can ...
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2answers
350 views

Plot Pareto tails in QQ-plot for log-normal distributions

I'm working on samples that I'm trying to fit into log-normal distributions. In some cases, Kolmogorov-Smirnov test statistics is something like D = 0.0056 with an associated p-value of 0. Hence, my ...
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BRT predictions on zero-inflated gaussian fish abundances include negative results

hopefully someone can point me in the right direction here. I'm using boosted regression trees (BRT) to assess the relative importance of a number of environmental factors (sea bottom temperature, ...
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35 views

Probabilities from lognormal distribution

If I have a variable x that is lognormal(mu=0, sd=.1), and say I want to compute P(x < .90) Can I then say P(x < .90) = P( log(x) < log(.90) ) ? Going by the book I am reading from, this ...
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70 views

Is the data normally or lognormally distributed?

I'm not sure how to give context to this question. We're to use Excel to analyze data and use log base 10 for each column of data that we analyze, which I'm not sure what they want here. Are they ...
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1answer
331 views

P-value NaN using chi2gof to validate lognormal distribution in dataset

I am trying to model a dataset of mine with a lognormal distribution using Matlab. I estimated the parameters via 'lognfit' and my generated datapoints with the fitted distribution look quite good ...