Parameters estimators of irregular right-angled triangular distribution

Kachiashvili, K. J.; Topchishvili, Alexander L.

doi:10.3233/mas-150362

Cited by 5 publications

(14 citation statements)

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“…The irregular right-angled triangular distribution discussed in [3] has two parameters a and b, where a is the lower limit and b is the upper limit, with the mode at b. The estimators proposed in [3], which are consistent, unbiased and efficient, are based on the order statistics of the experimental sample. Let x = (x 1 , .…”

Section: Introductionmentioning

confidence: 99%

“…, x n ) be the observed values of a sample of size n and let x (1) and x (n) be the smallest and the largest values, respectively. The estimators of [3] are based on â = x (1) and b = x (n) which are claimed to be maximum likelihood estimators (MLE). While it is true that b is a MLE, this is not the case of â.…”

Section: Introductionmentioning

confidence: 99%

“…While it is true that b is a MLE, this is not the case of â. For example, with the sample x = (0, 1) of size n = 2 the likelihood function of equation ( 3) in [3] is not maximized at a = 0 but rather the MLE is a * = −1/2. However, the simplicity of the estimators â = x (1) and b = x (n) together with their easily obtained expectations based on their respective tail distributions (1 − x 2 ) n and x 2n when a = 0 and b = 1, makes their unbiased versions quite attractive in practice.…”

Section: Introductionmentioning

confidence: 99%

“…However, the simplicity of the estimators â = x (1) and b = x (n) together with their easily obtained expectations based on their respective tail distributions (1 − x 2 ) n and x 2n when a = 0 and b = 1, makes their unbiased versions quite attractive in practice. Nonetheless, we feel that a brief analysis of the MLE estimator of the lower limit parameter a constitutes a useful complement to that of [3].…”

Section: Introductionmentioning

confidence: 99%

“…

Simple estimators were given in [3] for the lower and upper limits of an irregular right-angled triangular distribution together with convenient formulas for removing their bias. We argue here that the smallest observation is not a maximum likelihood estimator (MLE) of the lower limit and we present a procedure for computing an MLE of this parameter.

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confidence: 99%

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Note on “Parameters estimators of irregular right-angled triangular distribution”

Lamond

Zéphyr

2021

MAS

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Simple estimators were given in (Kachiashvili & Topchishvili, 2016) for the lower and upper limits of an irregular right-angled triangular distribution together with convenient formulas for removing their bias. We argue here that the smallest observation is not a maximum likelihood estimator (MLE) of the lower limit and we present a procedure for computing an MLE of this parameter. We show that the MLE is strictly smaller than the smallest observation and we give some bounds that are useful in a numerical solution procedure. We also present simulation results to assess the bias and variance of the MLE.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Note on “Parameters estimators of irregular right-angled triangular distribution”

Lamond

Zéphyr

2021

MAS

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Hybrid simplicial-randomized approximate stochastic dynamic programming for multireservoir optimization

Zephyr,

Lamond,

Lang

2024

Comput Manag Sci

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We revisit an approximate stochastic dynamic programming method that we proposed earlier for the optimization of multireservoir problems. The method exploits the convexity properties of the value function to sample the reservoir level space based on the local curvature of the value function, which is estimated by the difference between a lower and an upper bounds (error bound). Unlike the previous approach where the state space was exhaustively partitioned into full dimensional simplices whose vertices formed a discrete grid over which the value function was approximated, here we propose instead a new randomized approach for selecting the grid points from a small number of randomly sampled simplices from which an error bound is estimated. Results of numerical experiments on three literature test problems and simulated midterm reservoir optimization problems illustrate the advantages of the randomized approach which can solve models of higher dimensions than with the exhausitive approach.

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Randomized Simplicial Approximate Stochastic Dynamic Programming for Mid-term Reservoir Optimization

Zéphyr

Lamond²

2022

2022 8th International Conference on Control, Decision and Information Technologies (CoDIT)

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Parameters estimators of irregular right-angled triangular distribution

Cited by 5 publications

References 5 publications

Note on “Parameters estimators of irregular right-angled triangular distribution”

Note on “Parameters estimators of irregular right-angled triangular distribution”

Hybrid simplicial-randomized approximate stochastic dynamic programming for multireservoir optimization

Randomized Simplicial Approximate Stochastic Dynamic Programming for Mid-term Reservoir Optimization

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