An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data
Adegoke Taiwo Mobolaji,
Nicholas Pindar Dibal,
Yahaya Abdullahi Musa
Issue:
Volume 5, Issue 1, February 2019
Pages:
1-5
Received:
26 December 2018
Accepted:
15 February 2019
Published:
28 March 2019
Abstract: The Bayesian estimation of unknown variance of a normal distribution is examined under different priors using Gibbs sampling approach with an assumption that mean is known. The posterior distributions for the unknown variance of the Normal distribution were derived using the following priors: Inverse Gamma distribution, Inverse Chi-square distribution and Levy distribution of the unknown variance of a normal distribution and Gumbel Type II. R functions are developed to study the various statistical simulation samples generated from Winbugs.
Abstract: The Bayesian estimation of unknown variance of a normal distribution is examined under different priors using Gibbs sampling approach with an assumption that mean is known. The posterior distributions for the unknown variance of the Normal distribution were derived using the following priors: Inverse Gamma distribution, Inverse Chi-square distribut...
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About the Evaluation of the Effectiveness of Various Methods of Diagnosis, Prediction and Classification Presented in the Literature
Yury Mikhailovich Petrenko
Issue:
Volume 5, Issue 1, February 2019
Pages:
6-12
Received:
19 January 2019
Accepted:
19 March 2019
Published:
10 May 2019
Abstract: The literature presents a large number of very different ways to diagnose, predict and classify. In support of their usefulness and effectiveness, various parameters are often used, from a large number of them, which are not always necessary and sufficient, since they do not unequivocally characterize efficiency. The purpose of this work was to build a theory in which the characteristic parameters would be clearly defined, necessary and sufficient to identify and evaluate the effectiveness of the method itself and the databases to which this method was applied. On the basis of an objective analysis of all known parameters characterizing the effectiveness of various methods of diagnosing and predicting, necessary and sufficient conditions were determined for them that ensure the unambiguity of the conducted assessments of their effectiveness. Some examples have shown their effectiveness. Full unambiguity and certainty in the reflection of the effectiveness of any method of diagnosis and prediction is achieved only when all the parameters characterizing it are interconnected by one equation. The paper presents a set of such equations, from which it follows that the uniqueness of the evaluation of the effectiveness of any method is achieved only when it is reflected by a triad of characteristic basis parameters. Only such a triad of efficiency parameters, interconnected by characteristic equations obtained in theory, that is, in a deterministic way, can one achieve an unambiguous estimate of efficiency and its interpretation. It is important that the parameters characterizing the data arrays for which one or another method is tested can also act as basic parameters. On the basis of the equations obtained in the work, by means of the triad of basic parameters, all other parameters are determined, diversifying the efficiency. One of these triads includes sensitivity, specificity and accuracy, which in this combination uniquely determine efficiency. In this paper, from these positions, data of some works of recent years are analyzed.
Abstract: The literature presents a large number of very different ways to diagnose, predict and classify. In support of their usefulness and effectiveness, various parameters are often used, from a large number of them, which are not always necessary and sufficient, since they do not unequivocally characterize efficiency. The purpose of this work was to bui...
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