On Statistics Independent of a Complete Sufficient Statistic

Basu, Debabrata

doi:10.1007/978-1-4419-5825-9_14

Cited by 120 publications

(87 citation statements)

References 3 publications

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“…We demand: The fairness statistic F(Y) shall be independent of the sample mean E[Y] . The theorem by Basu [2] shows that sample variance and standard deviation fulfill this property and are independent from the sample mean. Therefore, we can concretize this property using the variance of QoE values.…”

Section: Desirable Properties Of a Qoe Fairness Indexmentioning

confidence: 95%

A new QoE fairness index for QoE management

et al. 2018

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The user-centric management of networks and services focuses on the Quality of Experience (QoE) as perceived by the end user. In general, the goal is to maximize (or at least ensure an acceptable) QoE, while ensuring fairness among users, e.g., in terms of resource allocation and scheduling in shared systems. A problem arising in this context is that the notions of fairness commonly applied in the QoS domain do not translate well to the QoE domain. We have recently proposed a QoE fairness index F, which solves these issues. In this paper, we provide a detailed rationale for it, along with a thorough comparison of the proposed index and its properties against the most widely used QoS fairness indices, showing its advantages. We furthermore explore the potential uses of the index, in the context of QoE management and describe future research lines on this topic.

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Section: Desirable Properties Of a Qoe Fairness Indexmentioning

confidence: 95%

A new QoE fairness index for QoE management

et al. 2018

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“…It can be shown that U 1 and U 2 are independent beta random variables with parameters (1, n − 1) and (1, m − 1), respectively, see [5]. Now…”

Section: Theorem 3 the Uniformly Minimum Variance Unbiased Estimator mentioning

confidence: 95%

Estimation of Stress-Strength Reliability for the Generalized Pareto Distribution Based on Progressively Censored Samples

2015

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This paper deals with the estimation of stress-strength reliability parameter, R = P (Y < X ), based on progressively type II censored samples when stress, strength are two independent generalized Pareto random variables. The maximum likelihood estimators, their asymptotic distributions, asymptotic confidence intervals, bootstrap based confidence intervals and Bayes estimators are derived for R. Using Monte Carlo simulations, the MSE, Bayes risk estimators, credible sets and coverage probabilities are computed and compared.

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“…Furthermore, by Cochran's theorem (Cochran, 1934) or Basu's theorem (Basu, 1955) it follows that, independently,…”

Section: Corrected Demand Distribution When Both µ and σ 2 Are Unknownmentioning

confidence: 99%

“…Basu (1955) discusses that two statistics are independently distributed if the first statistic is a sufficient statistic for a certain parameter and the distribution of the other statistic does not depend on that parameter. In this case the SMA estimator is a sufficient statistic for µ in the restricted sample consisting of the last M demand observations, and the distribution of the sample variance does not depend on µ.…”

Section: Corrected Demand Distribution When Both µ and σ 2 Are Unknownmentioning

confidence: 99%

On the calculation of safety stocks when demand is forecasted

Prak

Teunter

Syntetos

2017

European Journal of Operational Research

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The inventory control literature generally assumes that the demand distribution and all its parameters are known. In practical applications it is often suggested to estimate the demand variance either directly or based on the one-period ahead forecast errors. The variance of the lead time demand, essential for safety stock calculations, is then obtained by multiplying the estimated per-period demand variance by the length of the lead time. However, this is flawed, since forecast errors for different periods of the lead time are positively correlated, even if the demand process itself does not show (process) auto-correlation. As a result these traditional procedures lead to safety stocks that are too low. This paper presents corrected lead time demand variance expressions and reorder levels for inventory systems with a constant lead time where demand fluctuates around a constant level. Firstly, we derive the exact lead time forecast error of mean demand conditional on the true demand variance. Secondly, we derive for normally distributed demand the correct reorder level under uncertainty of both the demand mean and variance. We show how the results can be implemented in inventory models, and particularly discuss batch ordering policies combined with moving average and exponential smoothing forecasts. We find that traditional approaches can lead to safety stocks that are up to 30% too low and service levels that are up to 10% below the target.

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On Statistics Independent of a Complete Sufficient Statistic

Cited by 120 publications

References 3 publications

A new QoE fairness index for QoE management

A new QoE fairness index for QoE management

Estimation of Stress-Strength Reliability for the Generalized Pareto Distribution Based on Progressively Censored Samples

On the calculation of safety stocks when demand is forecasted

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