#statstab #451 Log-normal Distribution – A simple explanation

Thoughts: A simple and useful source for the log-normal distribution, which has many uses (as I will show in 2026 🤫)

#lognormal #distribution #exponentional #guide #pedagogy

https://towardsdatascience.com/log-normal-distribution-a-simple-explanation-7605864fb67c/

Log-normal Distribution – A simple explanation | Towards Data Science

How to calculate μ & σ, the mode, mean, median & variance

Towards Data Science

"A generalized linear model or #GLM consists of three components:
1. A random component, specifying the conditional distribution of the response variable, Yᵢ (for the ith of n independently sampled observations). […]
2. A linear predictor—that is a linear function of regressors,
ηᵢ = α + Σⱼ Xᵢⱼ*βⱼ
3. A smooth and invertible link function g(·), which transforms the expectation of the response variable, μᵢ ≡ E(Yᵢ), to the linear predictor:
g(μᵢ) = ηᵢ"

https://www.sagepub.com/sites/default/files/upm-binaries/21121_Chapter_15.pdf

#models #dataDev #logNormal #regression #normality #normalDistribution #gamma #modelling #modeling #AIDev #ML #evaluation

"In #probability theory, a log-normal (or #lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution."

"It is a convenient and useful model for measurements in exact and engineering sciences, as well as medicine, economics […], energies, concentrations, lengths, prices".

https://en.wikipedia.org/wiki/Log-normal_distribution

#statistics #finance #modeling

Log-normal distribution - Wikipedia

"The #gamma GLM is a relatively assumption-light means of #modeling non-negative data, given gamma's flexibility.
[…]
"Explaining what is used and what is not used, despite merits and demerits […]: Loosely, the larger the internal literature in any field on modelling techniques, the less inclined people in that field seem to be to try something different."

Nick Cox, 2013: https://stats.stackexchange.com/questions/67547/when-to-use-gamma-glms

#normality #normalDistribution #modelling #dataDev #AIDev #ML #AIEvaluation #logNormal

When to use gamma GLMs?

The gamma distribution can take on a pretty wide range of shapes, and given the link between the mean and the variance through its two parameters, it seems suited to dealing with heteroskedasticity...

Cross Validated

Time for another roundup of business at the  Open Journal of Astrophysics. This time I have three papers to announce, which brings the total we have published so far this year (Vol. 7) to 45 and the total published by OJAp to 160. We’re still on track to publish around 100 papers this year or more, compared to last year’s 50.

First one up, published on 3rd June 2024, is “Log-Normal Waiting Time Widths Characterize Dynamics” by Jonathan Katz of Washington University (St Louis, Missouri, USA). This paper presents a discussion of the connection between waiting time distributions and dynamics for aperiodic astrophysical systems, with emphasis on log-normal distributions.  This paper is in the folder marked High-Energy Astrophysical Phenomena.

Here is a screen grab of the overlay, which includes the abstract:

 

You can read the paper directly on arXiv here.

The second paper to present is “An Empirical Model For Intrinsic Alignments: Insights From Cosmological Simulations” by Nicholas Van Alfen (Northeastern University, Boston, USA), Duncan Campbell (Carnegie Mellon University, Pittsburgh, USA), Jonathan Blazek (Northeastern University), C. Danielle Leonard (Newcastle University, UK), Francois Lanusse (Université Paris-Saclay, France), Andrew Hearin (Argonne National Laboratory, USA), Rachel Mandelbaum (Carnegie Mellon University) and The LSST Dark Energy Science Collaboration.  This paper presents an extension of the halo model (specifically the Halo Occupation Distribution, HOD) to include intrinsic alignment effects for the study of weak gravitational lensing. This paper is in the folder marked Cosmology and Nongalactic Astrophysics. It was published on Tuesday June 4th 2024.

The overlay looks like this:

 

 

You can read this paper directly on the arXiv here.

Last, but by no means least, comes  “Towards Cosmography of the Local Universe”  which proposes the multipoles of the distance-redshift relation as new cosmological observables that have a direct physical interpretation in terms of kinematical quantities of the underlying matter flow. This was also published on 4th June. The authors are Julian Adamek (IfA Zurich, Switzerland), Chris Clarkson (Queen Mary, London, UK), Ruth Durrer (Geneva, Switzerland), Asta Heinesen (U. Lyon, France & NBI Copenhagen, Denmark), Martin Kunz (Geneva), and Hayley J. Macpherson (Chicago, USA).

Here is a screengrab of the overlay:

 

 

To read the accepted version of this on the arXiv please go here. This paper is also in the folder marked Cosmology and Nongalactic Astrophysics. That’s it for this week. I aim to post another update next weekend.

 

 

https://telescoper.blog/2024/06/08/three-new-publications-at-the-open-journal-of-astrophysics-9/

#aperiodicSystems #arXiv230305578v3 #arXiv231107374v2 #arXiv240212165v2 #cosmography #Cosmology #CosmologyAndNonGalacticAstrophysics #HaloModel #haloOccupationDistribution #HighEnergyAstrophysicalPhenomena #intrinsicAlignments #Lognormal #lognormalDistributions #OJAp #statistics #TheOpenJournalOfAstrophysics #waitingTimes #weakGravitationalLensing

Vol. 7, 2024 | Published by The Open Journal of Astrophysics

Papers published in 2024

Time for another roundup of business at the  Open Journal of Astrophysics. This time I have three papers to announce, which brings the total we have published so far this year (Vol. 7) to 45 and the total published by OJAp to 160. We’re still on track to publish around 100 papers this year or more, compared to last year’s 50.

First one up, published on 3rd June 2024, is “Log-Normal Waiting Time Widths Characterize Dynamics” by Jonathan Katz of Washington University (St Louis, Missouri, USA). This paper presents a discussion of the connection between waiting time distributions and dynamics for aperiodic astrophysical systems, with emphasis on log-normal distributions.  This paper is in the folder marked High-Energy Astrophysical Phenomena.

Here is a screen grab of the overlay, which includes the abstract:

 

You can read the paper directly on arXiv here.

The second paper to present is “An Empirical Model For Intrinsic Alignments: Insights From Cosmological Simulations” by Nicholas Van Alfen (Northeastern University, Boston, USA), Duncan Campbell (Carnegie Mellon University, Pittsburgh, USA), Jonathan Blazek (Northeastern University), C. Danielle Leonard (Newcastle University, UK), Francois Lanusse (Université Paris-Saclay, France), Andrew Hearin (Argonne National Laboratory, USA), Rachel Mandelbaum (Carnegie Mellon University) and The LSST Dark Energy Science Collaboration.  This paper presents an extension of the halo model (specifically the Halo Occupation Distribution, HOD) to include intrinsic alignment effects for the study of weak gravitational lensing. This paper is in the folder marked Cosmology and Nongalactic Astrophysics. It was published on Tuesday June 4th 2024.

The overlay looks like this:

 

 

You can read this paper directly on the arXiv here.

Last, but by no means least, comes  “Towards Cosmography of the Local Universe”  which proposes the multipoles of the distance-redshift relation as new cosmological observables that have a direct physical interpretation in terms of kinematical quantities of the underlying matter flow. This was also published on 4th June. The authors are Julian Adamek (IfA Zurich, Switzerland), Chris Clarkson (Queen Mary, London, UK), Ruth Durrer (Geneva, Switzerland), Asta Heinesen (U. Lyon, France & NBI Copenhagen, Denmark), Martin Kunz (Geneva), and Hayley J. Macpherson (Chicago, USA).

Here is a screengrab of the overlay:

 

 

To read the accepted version of this on the arXiv please go here. This paper is also in the folder marked Cosmology and Nongalactic Astrophysics. That’s it for this week. I aim to post another update next weekend.

 

 

https://telescoper.blog/2024/06/08/three-new-publications-at-the-open-journal-of-astrophysocs/

#aperiodicSystems #arXiv230305578v3 #arXiv231107374v2 #arXiv240212165v2 #cosmography #Cosmology #CosmologyAndNonGalacticAstrophysics #HaloModel #haloOccupationDistribution #HighEnergyAstrophysicalPhenomena #intrinsicAlignments #Lognormal #lognormalDistributions #OJAp #statistics #TheOpenJournalOfAstrophysics #waitingTimes #weakGravitationalLensing

Vol. 7, 2024 | Published by The Open Journal of Astrophysics

Papers published in 2024

Neurons in The Brain Appear to Follow a Distinct Mathematical Pattern

Researchers taking part in the Human Brain Project have identified a mathematical rule that governs the distribution of neurons in our brains.

ScienceAlert

Out of curiosity, I'd like to see the statistical distribution of birthdates I've provided to websites for age verification over the past 20 years. #lognormal

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Deth Veggie -=cDc=- (@dethveggie@mastodon.online)

Deth Veggie's First Rule of Internet is: LIE TO EVERY SITE ABOUT EVERYTHING YOU CAN.

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