On the Composition of Unimodal Distributions

Ибрагимов, И. А.

doi:10.1137/1101021

Cited by 282 publications

(125 citation statements)

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“…It is well known that quasi convexity is preserved for integral convolutions provided the distribution is strongly unimodal, a result due to Ibragimov (1956). For a simple proof, the reader is referred to Theorem 1.10 of Dharmadhikari and Joag-Dev (1988).…”

Section: The N-period Dynamic Modelmentioning

confidence: 96%

Optimal Inventory Policy with Two Suppliers

Fox

Metters

Semple

2006

Operations Research

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We analyze a periodic-review inventory model where the decision maker can buy from either of two suppliers. With the first supplier, the buyer incurs a high variable cost but negligible fixed cost; with the second supplier, the buyer incurs a lower variable cost but a substantial fixed cost. Consequently, ordering costs are piecewise linear and concave. We show that a reduced form of generalized s S policy is optimal for both finite and (discounted) infinite-horizon problems, provided that the demand density is log-concave. This condition on the distribution is much less restrictive than in previous models. In particular, it applies to the normal, truncated normal, gamma, and beta distributions, which were previously excluded. We concentrate on the situation in which sales are lost, but explain how the policy, cost assumptions, and proofs can be altered for the case where excess demand is backordered. In the lost sales case, the optimal policy will have one of three possible forms: a base stock policy for purchasing exclusively at the high variable cost (HVC) supplier; an s LVC S LVC policy for buying exclusively from the low variable cost (LVC) supplier; or a hybrid s S HVC S LVC policy for buying from both suppliers.

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Section: The N-period Dynamic Modelmentioning

confidence: 96%

Optimal Inventory Policy with Two Suppliers

Fox

Metters

Semple

2006

Operations Research

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“…For example, if a univariate density is log-concave, then it is unimodal; the corresponding survival function and distribution function are both log-concave. Ibragimov (1956) proved the equivalence of log-concavity and strong unimodality. For more about the theory of log-concave function see Bagnoli and Bergstrom (1988), An (1998) and Dharmadhikari and Joag-dev (1988).…”

Section: Resultsmentioning

confidence: 99%

On Minimally-supported D-optimal Designs for Polynomial Regression with Log-concave Weight Function

Chang

Lin

2006

Metrika

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“…(ii) Since each Y j is independent and log-concave, the convolution Y = j∈J Y j is log-concave (Ibragimov 1956). Denote the probability density function (pdf) of…”

Section: Proof Of Lemmamentioning

confidence: 99%

An iterative algorithm to bound partial moments

Muns

2018

Comput Stat

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This paper presents an iterative algorithm that bounds the lower and upper partial moments of an arbitrary univariate random variable X by using the information contained in a sequence of finite moments of X . The obtained bounds on the partial moments imply bounds on the moments of the transformation f (X ) for a certain function f : R → R. Two examples illustrate the performance of the algorithm.

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On the Composition of Unimodal Distributions

Cited by 282 publications

References 0 publications

Optimal Inventory Policy with Two Suppliers

Optimal Inventory Policy with Two Suppliers

On Minimally-supported D-optimal Designs for Polynomial Regression with Log-concave Weight Function

An iterative algorithm to bound partial moments

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