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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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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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1answer
39 views

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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Plot Cumulative Distribution Function of Kernel in R [closed]

I am trying to plot $\hat F(x)$ of the log-normal kernel in R. It is a simple $\hat F(x)$ log-normal distribution with some transformation proposed by Jin and Kawczak (2003) (Check here if needed). ...
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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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Is there a standard letter or symbol for the geometric mean? [closed]

Is there a standard letter or symbol for the geometric mean? For example, with a log-normal distribution parameterized with $\mu$ and $\sigma$, the geometric mean is $e^\mu$. What would be the most ...
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1answer
20 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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7 views

Sum of multivariate lognormals

Is it possible to approximate the sum of multivariate lognormals using Wilkinson approximation? Any reference?
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1answer
39 views

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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2answers
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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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1answer
40 views

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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42 views

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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0answers
41 views

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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What a log-normal distribution can tell me about my data?

I am currently working on social media data. When I first plotted the distribution of the data, I thought that it could be a power law distribution. However, the analysis which I carried out by using ...
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1answer
104 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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0answers
19 views

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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1answer
47 views

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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3answers
76 views

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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Derive wald test estimator lognormal distribution

$$\Delta = exp(\frac{\sum\limits_{i=1}^{n}logx_i}{n_2}+0.5\frac{\sum\limits_{i=1}^{n}(log(x_i)-\mu )^2}{n_2})/exp(\frac{\sum\limits_{i=1}^{n}logx_i}{n_1}+0.5\frac{\sum\limits_{i=1}^{n}(log(x_i)-\mu )^...
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Lognormal model assistance

I'm a product researcher and I'm working on a model of task completion times for a product. Since the task completion times will all be positive, I have LOG10 transformed them in Excel. I've then ...
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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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2answers
148 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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1answer
98 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
93 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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1answer
77 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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79 views

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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1answer
122 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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0answers
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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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1answer
22 views

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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0answers
83 views

When to use natural log transformation [duplicate]

Statistics noob working on a thesis here. I want to use this variable in a linear regression, so I performed a natural log transformation on it and the QQ-plot looks slightly better than the original (...
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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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1answer
43 views

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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1answer
38 views

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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1answer
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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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1answer
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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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1answer
175 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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1answer
37 views

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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3answers
60 views

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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1answer
65 views

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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0answers
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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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1answer
154 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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2answers
141 views

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
28 views

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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1answer
202 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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1answer
23 views

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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2answers
108 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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2answers
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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1answer
28 views

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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93 views

Time Series of Normal Distributions

An investor retires with a $1M portfolio and plans to spend a constant-dollar amount of \$40,000 annually from the portfolio. Should the annual withdrawal in any year exceed the remaining portfolio ...
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0answers
31 views

How dose probability have outcome become greater than 1? [duplicate]

I am doing a research to calculate the probability of transformers failure rate for each root causes. in order to do that I use probability distribution function that fit my data. one of the root ...
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139 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 ...