The Normal Curve and its Abnormalities

ERNEST G. POSER

doi:10.1037/0010606

The Subnormal Area Under the Normal Curve of Intelligence

Contemporary Psychology ◽

10.1037/008342 ◽

1968 ◽

Vol 13 (1) ◽

pp. 19-21

Author(s):

PAUL R. DOKECKI

Keyword(s):

Normal Curve

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The Charitable Continuum

Theoretical Inquiries in Law ◽

10.1515/til-2021-0011 ◽

2021 ◽

Vol 22 (1) ◽

pp. 285-334

Author(s):

Eric Kades

Keyword(s):

Central Limit Theorem ◽

Limit Theorem ◽

Social Welfare ◽

Normal Curve ◽

Charitable Donation ◽

Charitable Donations ◽

The Central Limit Theorem ◽

Central Value ◽

Fairness And Efficiency ◽

Better Than

Abstract There are powerful fairness and efficiency arguments for making charitable donations to soup kitchens 100% deductible. These arguments have no purchase for donations to fund opulent church organs, yet these too are 100% deductible under the current tax code. This stark dichotomy is only the tip of the iceberg. Looking at a wider sampling of charitable gifts reveals a charitable continuum. Based on sliding scales for efficiency, multiple theories of fairness, pluralism, institutional competence and social welfare dictate that charitable deductions should in most cases be fractions between zero and one. Moreover, the Central Limit Theorem strongly suggests that combining this welter of largely independent criteria with the wide variety of charitable gifts results in a classic bell-shaped normal curve of optimal deductions, with a peak at some central value and quickly decaying to zero at the extremes of 0% and 100%. Given that those are the only two options under the current tax code, the current charitable deduction regime inevitably makes large errors in most cases. Actually calculating a precise optimal percentage for each type of charitable donation is of course impractical. This Article suggests, however, that we can do much better than the systematically erroneous current charitable deduction. Granting a 100% deduction only for donations to the desperately poor, along with 50%, 25%, and 0% for gifts yielding progressively fewer efficiency, fairness, pluralism, and institutional competence benefits, promises to deliver a socially more desirable charitable deduction.

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The logistic distribution as an approximation to the normal curve

The Journal of the Acoustical Society of America ◽

10.1121/1.1913467 ◽

1973 ◽

Vol 53 (5) ◽

pp. 1296-1296 ◽

Cited By ~ 4

Author(s):

Lloyd A. Jeffress

Keyword(s):

Logistic Distribution ◽

Normal Curve

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A peaked logistic-based selection curve

Canadian Journal of Fisheries and Aquatic Sciences ◽

10.1139/cjfas-2013-0401 ◽

2014 ◽

Vol 71 (3) ◽

pp. 351-355 ◽

Cited By ~ 4

Author(s):

James A. Smith ◽

Matthew D. Taylor

Keyword(s):

Large Range ◽

Logistic Distribution ◽

Fishing Gear ◽

Normal Curve ◽

Logistic Curve ◽

Size Classes ◽

Logistic Equations ◽

Selection For

Length-based selection curves define the relative catchability of fish to specific types of fishing gear, with catchability often highest at intermediate fish lengths. Distributions such as the normal, lognormal, or gamma are often used to define “peaked” selection curves, but these have limited capabilities to describe strongly asymmetric selection relationships, such as those sometimes observed for hooks or gillnets. Another, more flexible, peaked selection curve is proposed, which is derived by combining multiple logistic distributions. While the logistic distribution is frequently used to describe monotonic selection curves, incorporating multiple logistic equations (that describe either the increasing or decreasing catchability) can define a large range of asymmetric peaked selection curves. This “peak-logistic” curve also allows nonzero asymptotic selection for the largest size classes, which may be the selection occurring in some hook-and-line fisheries. We demonstrate examples of selection in hook, haul net, and mixed hook fisheries, for which the peak-logistic curve is more appropriate than comparative lognormal and binormal selection curves. We also promote an alternative to the peak-logistic: the two-sided normal curve.

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