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The MLP Distribution: A Modified Lognormal Power-Law Model for the Stellar Initial Mass Function

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Shantanu Basu, M. Gil, Sayantan Auddy

Solar and Stellar Astrophysics · Submitted 27 Feb 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier (2005) and how this fit can be used to quickly identify quantities like the mean, median, and mode, as well as number and mass fractions in different mass intervals.

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arXiv ID1503.00023 (version 1)
Pith IDWQHW7TGM, Pith's permanent record of this paper and its review
CitationM. Gil, Sayantan Auddy, Shantanu Basu. "The MLP Distribution: A Modified Lognormal Power-Law Model for the Stellar Initial Mass Function." arXiv:1503.00023 (2015). https://pith.science/paper/WQHW7TGM
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,048 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.34 · mentions code or data availability 0.05.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. This leads to a modified lognormal with a power-law tail (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. These analytic properties of the distribution can be used to facilitate application to modeling the IMF. We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier (2005) and how this fit can be used to quickly identify quantities like the mean, median, and mode, as well as number and mass fractions in different mass intervals.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). contribution 0.99 0.84 0.10 asserted 0.96
s1 The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. method 0.65 0.12 0.07 asserted 1.00
s2 This leads to a modified lognormal with a power-law tail (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. interpretation 0.45 0.30 0.25 asserted 0.83
s3 We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. contribution 0.86 0.96 0.09 asserted 1.00
s4 These analytic properties of the distribution can be used to facilitate application to modeling the IMF. contribution 0.43 0.48 0.09 hedged possibility 0.60
s5 We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier (2005) and how this fit can be used to quickly identify quantities like the mean, median, and mode, as well as number and mass fractions in different mass intervals. result 0.91 0.94 0.58 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.89 · evidence from proof or derivation 0.63.

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. This leads to a modified lognormal with a power-law tail (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. These analytic properties of the distribution can be used to facilitate application to modeling the IMF. We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier (2005) and how this fit can be used to quickly identify quantities like the mean, median, and mode, as well as number and mass fractions in different mass intervals.

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