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Date: 20-4-2021
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The Mills ratio is defined as
(1) |
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(2) |
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(3) |
where is the hazard function, is the survival function, is the probability density function, and is the distribution function.
For example, for the normal distribution,
(4) |
which simplifies to
(5) |
for the standard normal distribution. The latter function has the particularly simple continued fraction representation
(6) |
(Cuyt et al. 2010, p. 376).
REFERENCES:
Boyd, A. V. "Inequalities for Mills' Ratio." Rep. Stat. Appl. Res. (Union Japan. Sci. Eng.) 6, 44-46, 1959.
Cuyt, A.; Brevik Petersen, V.; Verdonk, B.; Waadeland, H.; and Jones, W. B. Handbook of Continued Fractions for Special Functions. New York: Springer, 2010.
Evans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 3rd ed. New York: Wiley, p. 13, 2000.
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كيف تساهم الأطعمة فائقة المعالجة في تفاقم مرض يصيب الأمعاء؟
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مشروع ضخم لإنتاج الهيدروجين الأخضر يواجه تأخيرًا جديدًا
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المجمع العلمي يختتم دورته القرآنية في فن الصوت والنغم بالطريقة المصرية
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