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Questions tagged [lognormal]

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

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Probability density function units of the log-normal distribution

In a discussion on this forum lognormal distribution, standard-deviation and (physical) units the cumulative distribution function (PDF) of the lognormal distribution was analysed. The conclusion ...
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plnorm and log scale parameters

I have expenditure data in several regions, and for each of them i know mean expenditure, standard deviation and skewness in original scale. Since data are skewed i want to compute probability of ...
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good terminology for the parameters of a lognormal distribution?

Is there any good short terminology for the two parameters of a lognormal distribution? I have been using mean-log for $\mu$ and volatility for $\sigma$, where the lognormal variable $X$ has $\ln(X)$ ...
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Moment Generating Function for Lognormal Random Variable

I'm working through the proof of a lognormal random variable and am having some difficulty in moving through it. I understand the following: Our CDF is $\Phi(\frac{logx - \mu}{\sigma})$, and thus our ...
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What is the best point forecast for lognormally distributed data?

I believe that the values I am forecasting are lognormally distributed with log-mean $\mu$ and log-variance $\sigma^2$. I need a point forecast (i.e., a one-number summary) that minimizes the expected ...
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CDF at n of normal distribution to the nth power

I'm working with an equation that includes a normally distributed investment return R. I can find the Cumulative Distribution Function of R for the first period n=0. However, how do I derive the CDF ...
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Tests of normality - qq and Shapiro-Wilk

I am new to the world of stats... My data had a log normal distribution, so transformed by log to get it nearer normal distribution. This is real-world data. From here I want to establish if my data ...
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What comes after the geometric mean?

The geometric mean is a multiplicative alternative to the arithmetic mean, which we could call additive mean, thereby calling the geometric mean multiplicative mean. My question is the following: what ...
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What is the PDF for a log-log-normal distribution?

A log-log-normal distribution is a continuous probability distribution of a random variable whose logarithm logarithm $\ln(\ln(x))$ is normally distributed. What is the Probability Density Function ...
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How to generate samples of Poisson-Lognormal distribution

I would like to compute samples of the number of product purchased in a supermarket. I want to model it with a mixed Poisson lognormal distribution. Items purchased $x$ of a given consumer follow a ...
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31 views

Log-normalization of predictors

I have the following dependent and independent variables for my linear regression model. Since they are all in different scales (some of the are % others continuous variables), I was suggested to take ...
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Sum of multivariate lognormals

Is it possible to approximate the sum of multivariate lognormals using Wilkinson approximation? Any reference?
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Log Transformation in R

I need to transform my not normal distributed data to normal distributed variables. Therefore I need to log-transform them. Log10(x+1) has not worked to create a normal distribution. Therefore, I want ...
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Is “geometric mean” the same as “the first moment of the lognormal distribution”?

I would like to compare the results of two studies, one reporting "geometric mean diameter" and the other one reporting "the first moment of the lognormal size distribution". I am not sure whether the ...
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Scaling percentiles of log-normal distribution

I need help with this basic question. A study found that a variable is log-normal, with mean A and percentiles p1, p2 and p3 (could be 10%, 50% and 90%). Another study for a different group found ...
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Lognormal Distribution Probability

I'm dealing with this question, and i didn't understand should i use the $f(x)$ formula for lognormal distribution or can i calculate it with $z(P)$? Thank you for help. And i've found probability $1....
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How do I interpret the p-value from a Shapiro-Francia Test?

I have a situation where I have more than 50 samples in a given set of inputs and I cannot use the Shapiro-Wilk test as I don't have the numbers for the pyramid for $n>50$. I was then asked to use ...
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361 views

Understanding the shifted log-normal distribution

I have difficulties understanding why a third parameter (the shift) is necessary to describe the log-normal distribution. Let's say we have a normal random variable X, if I shift this variable by an ...
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Median versus Harmonic Mean As Log Normal Data Summary

I have a set of data that follows a lognormal distribution (it is fixed-distance, variable-speed situation https://stats.stackexchange.com/a/23130/55305). I am trying to summarize the data in a single ...
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Log transformation to generate random number producing NA's

I am trying to generate a random values using log distribution. The reason for using log-distribution is keep the values positive. ...
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Log-normal returns

Let $P_t$ denote a stock price distributed as $\operatorname{lognormal}(\mu , \sigma^2 )$. Suppose we construct simple returns $R_t=\frac{P_t-P_{t-1}}{P_{t-1}}$. My question is: What is the ...
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Approximating the first moment of $h(x)$ where $x$ ~${\rm log\,normal}(\mu, \sigma)$

What is the best way to approximate $E(h(X))$, where $X$ ~ Lognomal($\mu, \sigma$)? So far, I can think of Monte Carlo Methods and Gaussian Hermite quadrature as below: \begin{align} E(h(X)) &= ...
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293 views

Application of Skewness and Kurtosis

Often in finance, stock prices are considered to follow a lognormal distribution while stock returns are considered to follow a normal distribution -prices are positive while returns can be negative(...
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103 views

Statistical analysis on confidence intervals

I have a data set where the data, when plotted, is not normal. Log-transforming the data makes it normal. Should confidence intervals for the population mean and hypotheses testing about the ...
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1answer
106 views

Sampling Methods/Monte Carlo method and Log-normal distribution

I found a problem from some notes i found online, here is a screenshot: I am trying to understand this question, it seems this function they define as the LIP() function is basically the quartile/...
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227 views

Fitting data to a log-normal distribution [duplicate]

For a simulation study I've been trying to find an appropriate distribution for job handling times in R. I have a very large dataset of 77010 records (handling time in seconds). I've been exploring ...
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Comparing two lognormal distributions

I have two lognormal distributions which represent the annual distribution of sales of fiction and non-fiction books, respectively. The sample size of fiction books is much larger than that of non-...
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251 views

Coefficient of variation (CV) of log-transformed data

I understand that with log-transformed data, the coefficient of variation (CV) on the original scale is equal to sqrt(exp(sigma^2)-1), where sigma is the standard ...
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Statistics of Extremes: Fitting the GEV distribution with MLE vs L-moments

I created a synthetic series that is supposed to simulate a series of peak discharges in blocks of years in arid catchments. The magnitudes were simulated via the Lnorm dist.: ...
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How to find the area undernearth a log-normal curve

I wanted to find the area underneath a Gaussian distribution. I found online that for an equation of the form: $Ne^{-\frac{(x-\mu)^2}{2\sigma^2}}$ The area under the curve is given by: $N \sigma \...
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Break down values in dataset to match mean and variance of another dataset

Vector A contains m variables that are log-normal distributed with mean $\mu_A$ and standard deviation $\sigma_A$. Vector B contains n variables that are log-normal distributed with mean $\mu_B$ and ...
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Hellinger distance for two shifted log-normal distributions

If I am not mistaken, Hellinger distance between P and Q is generally given by: $$ H^2(P, Q) = \frac12 \int \left( \sqrt{dP} - \sqrt{dQ} \right)^2 .$$ If P and Q, however, are two differently ...
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From log-normal parameters, to normal parameters

from the following log-normal fitting function (https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html), I get the parameters [s, loc and scale]. How can I use them to get the μ ...
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Is this notation for a lognormally distributed variable misleading?

I have gotten into the habit of notating a lognormally distributed random variable $X$ as: $$X \sim \ln\mathcal{N}(\mu,\sigma^2)$$ I am now starting to question where I picked this habit up and ...
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Difference between log normal probability density values

just reviewing two resources, I noticed a difference between the log normal p.d values : One is here which takes the e to the power in which it contains ln(x) the other is here Which on page 5 , ...
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227 views

Logarithmic binning and log-normal distribution

I've an Italian cities dataset. It's similar to those British ones used in literature, but has some differences, though. I decided to perform a logarithmic binning to avoid noise on the right end of ...
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Python np.lognormal gives infinite results for big average and St Dev

I am trying to draw the lognormal distribution for my data. using the following code : ...
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Why is the price of a security after $n$ intervals of additional time modeled using a lognormal distribution?

I am reading a book about financial mathematics. There's a problem in the book that says that if $S(n)$ denotes the price of a certain security at the end of $n$ additional weeks, we can model the ...
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Lognormal and normal distributions

I have a dataset, X, of real numbers, x, that I assume they follow a Lognormal distribution. Based on this, the distribution <...
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Log-normal vs. log-linear vs. logging the response variable

I've been reading a lot of Wikipedia pages and StackExchange/CrossValidated posts, and I have come to a point where I realize I do not understand some of the terminology I have been using. What's ...
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222 views

Should R squared value be changing when both predictions and actual values are transformed together?

I have a regression prediction task where my outcome variable is right skewed. I performed a log transformation of the outcome variable and put it in a linear regression model. I assessed the R ...
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Log-normal density function using rlnorm() in R

I tried to draw a log-normal density function by generating random numbers in R. However, the function is not working how I think it should. I draw two similar distribution using two different sample ...
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1answer
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Need handy formula for $\text{Cov}[\max(V_1-K_1,0), \max(V_2-K_2, 0)]$

In a recent post, I asked for help deriving a computable formula for $\text{Var}[\max(V-K,0)]$ based on the approach on p. 262 of ths book. $V$ is a lognormally distributed random variable and $K$ is ...
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275 views

How to improve fit of distribution to data

I'm trying to fit one of common expenential distributions to data using histfit. However it seems that results aren't as good as expected - it seems that peak should be higher. Histograms presents ...
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Given coefficients of a linear regression, how can I calculate what coefficients would be with log(y)?

Is there a way to analytically determine the new coefficients without re-estimating the regression? To give you a concrete example that might make answering easier, consider the following two models. ...
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115 views

Need handy formula for $Var[\max(V, K)]$

In Appendix 12A, p. 262 of this book, the author Hull derives a handy, tractable formula for the expression $E[\max(V-K, 0)]$, where $V$ is a lognormally distributed random variable and $K$ is a ...
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41 views

General way to calculate or think about non-linear but monotonic (?) transforms of random variables

I am doing a lot of work with lognormal RVs. I am trying to get my head around the formal mathematics of the non-linear transform of a random variable, particularly where there isn't any '...
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Does a 3-variable log-normal, with offset, continue to generate log-normals when multiplied by a log-normal?

Suppose I am trying to estimate a future population that I believe to be log-normally distributed from a current value. But, every $n$ periods, I remove a fixed amount in the future. For example, ...
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164 views

How do I interpret the posterior in a GLM of the lognormal family?

How do I interpret the posterior in a GLM of the lognormal family? I collected some data that is bound at zero and skewed to the left. I therefore assumed Y to be lognormal distributed and run a ...
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1answer
38 views

Power transformation of OU process

Say I have $X$ that follows an Ornstein-Uhlenbeck process: $$ dX_t = \phi (\mu - x_t) d_t + \sigma d W_t $$ Let $Y_t = \exp(X_t)$. Is there anything that helps me compute $\lim_{t\to\infty}E[Y_t^\...