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

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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\{ \sum_{i = 1}^n k_i \exp\left\{a_i x ...
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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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39 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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30 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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18 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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104 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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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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31 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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56 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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39 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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“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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36 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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32 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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76 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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31 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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43 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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81 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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49 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
28 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
30 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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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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67 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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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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225 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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32 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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64 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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203 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 ...
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85 views

Lognormal with negative values

I have some logged increments from time series data and wanted to fit a lognormal distribution, but obviously some are negative. How can I do this?
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How to calculate the degree of freedom in probability distribution fitting?

I am not familiar with degree of freedom. Here are some related questions: Assume $x$ follows $lognormal$ distribution: $x$~$lognormal(\mu,\theta)$. Fit a dataset {$x$} (with $N$ $x$'s). What is the ...
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How would you visualize the difference between Cox/Weibull regression?

I'm trying to figure a way of properly displaying the difference\resemblance between various regression values on the same data set, using cox ph, weibull regression and log-normal regression. ...
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Which has the heavier tail, lognormal or gamma?

(This is based on a question that just came to me via email; I've added some context from a previous brief conversation.) Last year I was told that the gamma distribution is heavier tailed than the ...
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Transformation of random variable - lognormal distribution

I'm answering questions from a book that I own and I'm left scratching my head because one of my answers does not match the one provided in the book. Either the book contains a typo or I've simply ...
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Approximation to Lognormal Distribution

I'm looking for an approximation to the curve of a lognormal distribution, for use in non-linear regression against a dataset. As an alternative, I'm interested in an approximation to the CDF thereof. ...
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Radial profile and 2d log-normal distribution?

I have a case study where a person should be located. We do not know where this person is, but we have some information. The total story is basically about the person which is to be searched. The ...
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1answer
85 views

What is the formula for lognormal hazard?

I'm plotting a bunch of survivor and hazard curves. The lognormal survivor function is: $S(t)=1-\Phi(\frac{log(t)-\mu}{\sigma}) $ Where $\mu$ is the scalar parameter. From a website ...
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55 views

how do i tranform my ols equation into logs?

Hi i'm reading threw all my statistics notes and i can't find any mention of how to transform ols variables into logs. ie i can't see a equation or any method of turning a beta value into a log form. ...
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79 views

relationship between normal and log-normal distribution

In wikipedia it is stated that: If $X \sim \operatorname{Log-\mathcal{N}}(\mu, \sigma^2)$ is distributed log-normally, then $\ln(X) \sim \mathcal{N}(\mu, \sigma^2)$ is a normal random variable. ...
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Interpretation of regression with independent variables as percentage

We have a list of indicators, say rates of selected ingredients sold, by 30 units over time. Over the last few years the rates for some indicators have changed but the question we want to ask is, have ...
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303 views

Variables lack correlation, but have pattern

Below is the graph of two variables, X and Y, each representing count data. N=348. Note the scales of the axes: Y is very approximately lognormal, but X has no decent fit (including Poisson, ...
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845 views

How to calculate a mean and standard deviation for a lognormal distribution using 2 percentiles

I am trying to calculate a mean and standard deviation from 2 percentiles for a lognormal distribution. I was successful in performing the calculation for a normal distribution using ...
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Log-normal model learning optimization

I am trying to model a variable (V) as a log normal distribution. $$ V = \mu \cdot\eta\,, \ \text{where } \eta \text{ is log normal} $$ Then $$ \ln V = ln(\mu) +\xi \\\\\text{where} \ \ \ \xi \ ...
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Using the log versus the level variable in Heckman second stage

Consider the Heckman selection model where my dependent variable is in log form for the second stage. I want to find the difference in computing derivative of unconditional expectation when using the ...
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72 views

How can the formula for the expectation of a log-normal random variable be dimensionally sound?

If $X\sim\mathcal{LN}({\mu,\sigma^2})$, then $\mathrm{E}[X]=e^{\mu+\sigma^2/2}$. My question is: what right do we have to add a mean and variance together? If $X$ has physical dimensions, then the ...
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Skew of log-normal distribution using sciPy

I am doing bioinformatics and I am trying to fit some values to a log-normal distribution with python's sciPy version 0.11. According to the skew of the resulting ...
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How to calculated Confidence Interval for autocorrelated and lognormally distributed data?

My data is autocorrelated and is lognormally distributed, how can I calculate Confidence interval of that set of data?
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Gamma vs. lognormal distributions

I have an experimentally observed distribution that looks very similar to a gamma or lognormal distribution. I've read that the lognormal distribution is the maximum entropy probability distribution ...
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Difference powerlaw, lognormal and stretched exponential (Weibull) function

I am currently fitting above mentioned functions to my data and I can observe, that both lognormal and Weibull are better fits than a power-law. In the literature it is often suggested that it is hard ...