scholarly journals Non-Parametric Probability Distributions Embedded Inside of a Linear Space Provided with a Quadratic Metric

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1901
Author(s):  
Pierpaolo Angelini ◽  
Fabrizio Maturo
Keyword(s):  
Social Sciences ◽  
Linear Space ◽  
Random Quantity ◽  
Probability Distributions ◽  
Statistical Sampling ◽  
Intrinsic Properties ◽  
Measurable Set ◽  
Geometric Entity ◽  
Closed Structure ◽  
Non Parametric

There exist uncertain situations in which a random event is not a measurable set, but it is a point of a linear space inside of which it is possible to study different random quantities characterized by non-parametric probability distributions. We show that if an event is not a measurable set then it is contained in a closed structure which is not a σ-algebra but a linear space over R. We think of probability as being a mass. It is really a mass with respect to problems of statistical sampling. It is a mass with respect to problems of social sciences. In particular, it is a mass with regard to economic situations studied by means of the subjective notion of utility. We are able to decompose a random quantity meant as a geometric entity inside of a metric space. It is also possible to decompose its prevision and variance inside of it. We show a quadratic metric in order to obtain the variance of a random quantity. The origin of the notion of variability is not standardized within this context. It always depends on the state of information and knowledge of an individual. We study different intrinsic properties of non-parametric probability distributions as well as of probabilistic indices summarizing them. We define the notion of α-distance between two non-parametric probability distributions.

scholarly journals Probability distributions for explaining hydrological losses in South Australian catchments

2013 ◽  
Vol 10 (4) ◽  
pp. 4597-4626
Author(s):  
S. H. P. W. Gamage ◽  
G. A. Hewa ◽  
S. Beecham
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Joint Probability ◽  
Accurate Estimation ◽  
Rainfall Runoff ◽  
Design Flood ◽  
Wide Variability ◽  
Multiple Variables ◽  
Two Parameter ◽  
Non Parametric

Abstract. The wide variability of hydrological losses in catchments is due to multiple variables that affect the rainfall-runoff process. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall-runoff models. Using representative single values of losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. Probability distributions can be used as a better representation of losses. In particular, using joint probability approaches (JPA), probability distributions can be incorporated into hydrological loss parameters in design models. However, lack of understanding of loss distributions limits the benefit of using JPA. The aim of this paper is to identify a probability distribution function that can successfully describe hydrological losses in South Australian (SA) catchments. This paper describes suitable parametric and non-parametric distributions that can successfully describe observed loss data. The goodness-of-fit of the fitted distributions and quantification of the errors associated with quantile estimation are also discussed a two-parameter Gamma distribution was identified as one that successfully described initial loss (IL) data of the selected catchments. Also, a non-parametric standardised distribution of losses that describes both IL and continuing loss (CL) data were identified. The results obtained for the non-parametric methods were compared with similar studies carried out in other parts of Australia and a remarkable degree of consistency was observed. The results will be helpful in improving design flood applications.

A Novel Tissue Characterisation Method Using Non-Parametric Compound Probability Distributions

2011 ◽  
Vol 37 (8) ◽  
pp. S154-S155
Author(s):  
N. Biberidis ◽  
A. Totorica ◽  
M. Pereyra ◽  
J. George ◽  
H. Batatia
Keyword(s):  
Probability Distributions ◽  
Tissue Characterisation ◽  
Compound Probability ◽  
Non Parametric

scholarly journals A characterization of normed M-spaces

1983 ◽  
Vol 24 (1) ◽  
pp. 89-92 ◽  
Author(s):  
Garfield C. Schmidt
Keyword(s):  
Linear Space ◽  
Linear Structure ◽  
Topological Spaces ◽  
Intrinsic Properties ◽  
Small Step ◽  
Linear Lattice ◽  
Linear Spaces ◽  
And Topology ◽  
Necessary And Sufficient

Linear spaces on which both an order and a topology are defined and related in various ways have been studied for some time now. Given an order on a linear space it is sometimes possible to define a useful topology using the order and linear structure. In this note we focus on a special type of space called a linear lattice and determine those lattice properties which are both necessary and sufficient for the existence of a classical norm, called an M-norm, for the lattice. This result is a small step in a program to determine which intrinsic order properties of an ordered linear space are necessary and sufficient for the existence of various given types of topologies for the space. This study parallels, in a certain sense, the study of purely topological spaces to determine intrinsic properties of a topology which make it metrizable and the study of the relation between order and topology on spaces which have no algebraic structure, or. algebraic structures other than a linear one.

scholarly journals Metode Mimicry-Memorization (Mim-Mem Method) dalam Meningkatkan Penguasaan Mufrodat Peserta Didik di Madrasah

PALAPA ◽  
2018 ◽  
Vol 6 (1) ◽  
pp. 90-110
Author(s):  
Syarifah Aini ◽  
Mualim Wijaya
Keyword(s):  
Social Sciences ◽  
Data Collection ◽  
Arabic Language ◽  
Test Method ◽  
Speaking Test ◽  
The Social ◽  
Method Student ◽  
Non Parametric

This research presented “influence method of mimicrymemorization(Mim-Mem Method) toward Mastery of vacabulary in Madrasah Aliyah Darul Lughah Wal Karomah”. The purpose of this method is to make easily undesrtanding and Master of Vocabulary to student into arabic language lesson. The first step is the teacher pronounce the words then repeated by students. This research was experimental. Whereas the data collection used speaking test method with comparative analyst technique (Non-Parametric) Mann-Whitney U-test (Uji U). To prove this research is significant or not, researchers use SPSS (Statistical Package for the Social Sciences). As for the result Mimicry-Memorization method (Mim-Mem Method) has affected to Vocabulary mastery in Madrasah Aliyah darul Lughah Wal Karomah. By using that method, student will be more active and more effective in learning arabic language lesson.

scholarly journals A symmetric divergence measure and its bounds

2011 ◽  
Vol 42 (4) ◽  
pp. 493-503
Author(s):  
K. C. Jain ◽  
Ruchi Mathur
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Divergence Measure ◽  
Numerical Illustration ◽  
Divergence Measures ◽  
Non Parametric

A new symmetric divergence measure is proposed which is useful in comparing two probability distributions. This non-parametric measure belongs to the Csiszar's $f$ divergence class. Its properties are studied and bounds are obtained in terms of some well known divergence measures. A numerical illustration based on the probability distribution is carried out.

scholarly journals A non-parametric hidden Markov model for climate state identification

2003 ◽  
Vol 7 (5) ◽  
pp. 652-667 ◽  
Author(s):  
M. F. Lambert ◽  
J. P. Whiting ◽  
A. V. Metcalfe
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Probability Distributions ◽  
Parametric Model ◽  
The State ◽  
Conditional Distributions ◽  
Wet And Dry Cycles ◽  
Non Parametric

Abstract. Hidden Markov models (HMMs) can allow for the varying wet and dry cycles in the climate without the need to simulate supplementary climate variables. The fitting of a parametric HMM relies upon assumptions for the state conditional distributions. It is shown that inappropriate assumptions about state conditional distributions can lead to biased estimates of state transition probabilities. An alternative non-parametric model with a hidden state structure that overcomes this problem is described. It is shown that a two-state non-parametric model produces accurate estimates of both transition probabilities and the state conditional distributions. The non-parametric model can be used directly or as a technique for identifying appropriate state conditional distributions to apply when fitting a parametric HMM. The non-parametric model is fitted to data from ten rainfall stations and four streamflow gauging stations at varying distances inland from the Pacific coast of Australia. Evidence for hydrological persistence, though not mathematical persistence, was identified in both rainfall and streamflow records, with the latter showing hidden states with longer sojourn times. Persistence appears to increase with distance from the coast. Keywords: Hidden Markov models, non-parametric, two-state model, climate states, persistence, probability distributions

Sign in / Sign up

Export Citation Format

Share Document