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Determining disease attributes from epidemic trajectories. [PDF]

Infect Dis Model
Rast MP, Rast LI.
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Repeated integrals of the univariate normal as a finite series with the remainder in terms of Moran's functions

Statistics, 2012
Laplace gave a divergent expansion for Mills’ ratio. Truncated to k terms, a bound is known for the remainder. We extend this result to repeated integrals of the normal density. Taylor series are also given for these.
Christopher S. Withers, Saralees Nadarajah   +1 more
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A remainder estimate for the normal approximation of perturbed sample quantiles

Statistics & Probability Letters, 1992
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Remainder term estimate for the asymptotic normality of the number of renewals

Journal of Applied Probability, 1980
It is well known that the number of renewals in the time interval [0, t] for an ordinary renewal process is approximately normally distributed under general conditions. We give a remainder term estimate for this normal distribution approximation.
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Monotonicity results of ratio between two normalized remainders of Maclaurin series expansion for square of tangent function

Mathematica Slovaca
Abstract In the paper, in view of the monotonicity rule for the ratio between two Maclaurin power series and by virtue of establishment of a monotonicity result for a sequence involving the ratio between two Bernoulli numbers, the authors investigate the monotonicity of the ratio between two normalized remainders of the Maclaurin power ...
Liu, Xin-Le, Qi, Feng
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Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function

Mathematica Slovaca
Abstract In the paper, by establishing an integral representation of a specific Maclaurin power series and in light of two monotonicity rules, the authors present very elegant proofs for several basic properties, including the positivity, (absolute) monotonicity, logarithmic convexity, and inequalities, of the normalized remainders of
Yue-Wu Li, Feng Qi
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Some properties of normalized remainders of the Maclaurin expansion for a function originating from an integral representation of the reciprocal of the gamma function

Mathematical Inequalities & Applications
Summary: It is well known that the classical Euler gamma function \(\Gamma (z)\) has had very extensive applications in mathematical sciences, including physics and engineering, in the past centuries. In this study, the authors introduce the normalized remainder \(T_{2n+1} [\Phi (\theta)]\) of the Maclaurin expansion of the function \(\Phi (\theta) = 1-
Zhang, Juan, Qi, Feng
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