scholarly journals Local linear conditional cumulative distribution function with mixing data

2019 ◽  
Vol 9 (2) ◽  
pp. 289-307 ◽  
Author(s):  
Oussama Bouanani ◽  
Saâdia Rahmani ◽  
Larbi Ait-Hennani
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Time Series Analysis ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
The Other ◽  
Cumulative Distribution ◽  
Mixing Conditions ◽  
Local Polynomial ◽  
Analysis Models

Abstract This paper investigates a conditional cumulative distribution of a scalar response given by a functional random variable with an $$\alpha $$ α -mixing stationary sample using a local polynomial technique. The main purpose of this study is to establish asymptotic normality results under selected mixing conditions satisfied by many time-series analysis models in addition to the other appropriate conditions to confirm the planned prospects.

scholarly journals On Distribution Characteristics of a Fuzzy Random Variable

2018 ◽  
Vol 47 (2) ◽  
pp. 53-67 ◽  
Author(s):  
Jalal Chachi
Keyword(s):  
Probability Theory ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Distribution Characteristics ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

scholarly journals Nondecreasing Lower Bound on the Poisson Cumulative Distribution Function for z Standard Deviations Above the Mean

2013 ◽  
Vol 50 (4) ◽  
pp. 909-917
Author(s):  
M. Bondareva
Keyword(s):  
Distribution Function ◽  
Lower Bound ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Step Function ◽  
Cumulative Distribution ◽  
Control Parameters ◽  
Poisson Random Variable ◽  
The Mean ◽  
Standard Deviations

In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean λ, where z and λ are parameters. This is important because the normal distribution as an approximation for the Poisson CDF may overestimate or underestimate its value. A sharp nondecreasing lower bound in the form of a step function is constructed. As a corollary of the bound's properties, for a given percent α and parameter λ, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to λ, its αth percentile is at most z standard deviations above its mean. For Poisson distributed control parameters, the corollary allows simple policies measuring performance in terms of standard deviations from a benchmark.

ON CUMULATIVE RESIDUAL EXTROPY

2019 ◽  
Vol 34 (4) ◽  
pp. 605-625 ◽  
Author(s):  
S. M. A. Jahanshahi ◽  
H. Zarei ◽  
A. H. Khammar
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Alternative Measure ◽  
Numerical Examples ◽  
Cumulative Residual ◽  
Measure Of Uncertainty

Recently, an alternative measure of uncertainty called extropy is proposed by Lad et al. [12]. The extropy is a dual of entropy which has been considered by researchers. In this article, we introduce an alternative measure of uncertainty of random variable which we call it cumulative residual extropy. This measure is based on the cumulative distribution function F. Some properties of the proposed measure, such as its estimation and applications, are studied. Finally, some numerical examples for illustrating the theory are included.

Quantifying variation of geomagnetic index empirical distribution and burst statistics across successive solar cycles.

2021 ◽  
Author(s):  
Aisling Bergin ◽  
Sandra Chapman ◽  
Nicholas Moloney ◽  
Nicholas Watkins
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Solar Cycle ◽  
Space Weather ◽  
Cumulative Distribution Function ◽  
Functional Form ◽  
Solar Maximum ◽  
Cumulative Distribution ◽  
Solar Cycles ◽  
Geomagnetic Index

<p>Impacts of space weather include possible disruption to electrical power systems, aviation, communication systems, and satellite systems. The climate of space weather is modulated by the solar cycle. The overall level of solar activity, and the response at earth, varies within and between successive solar cycles. Quantifying space weather risk requires understanding how the occurrence frequency of events of a given size varies with the strength of each solar cycle.<br>    The auroral electrojet index (AE) is a geomagnetic index which parameterises high latitude geomagnetic response at earth. We consider non-overlapping 1 year samples of AE at different solar cycle phases. We use data-data quantile-quantile plots to identify the 75th quantile as the threshold between two physical components in the cumulative distribution function. The bulk of the distribution lies below the threshold, while above it is the long tail. The magnitude of 75th quantile threshold scales with overall solar cycle activity level. At solar maximum, the 75th quantile relates to events which exceed 160 - 350 nT. We find that above the 75th quantile of observed data records, there exists an underlying functional form for the tail of the cumulative distribution function which does not change from one solar maximum to the next.<br>    Bursts, or excursions above a fixed threshold in the AE index time series, characterise space weather events. We perform the first study of variation in AE burst statistics within and between the last four solar cycles. We will discuss burst statistics for solar cycle maximum, minimum and declining phases. We find that, for bursts above 75th quantile thresholds, the functional form of the burst return period distribution is stable over successive solar maxima. A key result of crossing theory is that time series-averaged burst return period and duration are related to each other via the cumulative distribution function of raw observations. If the overall amplitude of the upcoming solar maximum can be predicted, our results may be used to provide constraints on the upcoming distribution of event return times.</p>

scholarly journals Intelligent Setting Method of Reagent Dosage Based on Time Series Froth Image in Zinc Flotation Process

Processes ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 536 ◽  
Author(s):  
Zhaohui Tang ◽  
Liyong Tang ◽  
Guoyong Zhang ◽  
Yongfang Xie ◽  
Jinping Liu
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Kernel Function ◽  
Bubble Size ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Dynamic Feature ◽  
Flotation Process ◽  
Feature Vectors ◽  
Froth Image

It is well known that the change of the reagent dosage during the flotation process will cause the froth image to change continuously with time. Therefore, an intelligent setting method based on the time series froth image in the zinc flotation process is proposed. Firstly, the sigmoid kernel function is used to estimate the cumulative distribution function of bubble size, and the cumulative distribution function shape is characterized by sigmoid kernel function parameters. Since the reagent will affect the froth image over a period of time, the time series of bubble size cumulative distribution function is processed by the ELMo model and the dynamic feature vectors are output. Finally, XGBoost is used to establish the nonlinear relationship modeling between reagent dosage and dynamic feature vectors. Industrial experiments have proved the effectiveness of the proposed method.

Nondecreasing Lower Bound on the Poisson Cumulative Distribution Function for z Standard Deviations Above the Mean

2013 ◽  
Vol 50 (04) ◽  
pp. 909-917
Author(s):  
M. Bondareva
Keyword(s):  
Distribution Function ◽  
Lower Bound ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Step Function ◽  
Cumulative Distribution ◽  
Control Parameters ◽  
Poisson Random Variable ◽  
The Mean ◽  
Standard Deviations

In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean λ, where z and λ are parameters. This is important because the normal distribution as an approximation for the Poisson CDF may overestimate or underestimate its value. A sharp nondecreasing lower bound in the form of a step function is constructed. As a corollary of the bound's properties, for a given percent α and parameter λ, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to λ, its αth percentile is at most z standard deviations above its mean. For Poisson distributed control parameters, the corollary allows simple policies measuring performance in terms of standard deviations from a benchmark.

scholarly journals Estimasi Fungsi Survival dan Fungsi Hazard Kumulatif Pada Data Survival Pederita Multiple Myeloma Serta Faktor-faktor yang Mempengaruhi Waktu Survivalnya

Intersections ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 33-43
Author(s):  
Toto Hermawan ◽  
Dwi Nurrohmah ◽  
Ismi Fathul Jannah
Keyword(s):  
Multiple Myeloma ◽  
Distribution Function ◽  
Data Analysis ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Hazard Function ◽  
Cumulative Distribution Function ◽  
Survival Function ◽  
Random Variable ◽  
Cumulative Distribution

Multiple myeloma is an infectious disease characterized by the accumulation of abnormal plasma cells, a type of white blood cell, in the bone marrow. The main objective of this data analysis is to investigate the effect of Bun, Ca, Pcells and Protein risk factors on the survival time of multiple myeloma patients from diagnosis to death. In the survival data analysis, the observed random variable T is the time needed to achieve success. To explain a random variable, the cumulative distribution function or the probability density function can be used. In survival analysis, the function of the random variable that becomes important is the survival function and the hazard function which can be derived using the cumulative distribution function or the probability density function. In general, it is difficult to determine the survival function or hazard function of a population group with certainty. However, the survival function or hazard function can still be approximated by certain estimation methods. The Kaplan-Meier method can be used to find estimators of the survival function of a population. Meanwhile, to find the estimator of the cumuative hazard function, the Nelson-Aalen method can be used. From the variables studied, it turned out that the one that gave the most significant effect was the Bun variable, namely blood urea nitrogen levels using both the exponential and weibull distribution. However, by using the weibull distribution, the presence of Bence Jones Protein in urine also has a quite real effect

scholarly journals Constructing a New Exponentiated Family Distribution with Reliability Estimation

2018 ◽  
Vol 29 (2) ◽  
pp. 155
Author(s):  
Shurooq Ahmed Al-Sultany
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Reliability Estimation ◽  
Least Square ◽  
Cumulative Distribution ◽  
New Family ◽  
Regression Approach ◽  
Two Parameters ◽  
The Given

This paper deals with using one method for transforming two parameters given distribution to another form with three parameters distribution, through using idea of reparameterization with powering the given cumulative distribution function by new parameter, where this work gives a new family through using new parameter which is necessary for generating values of the r.v from given CDF through smoothing the values of the given random variable to obtain new values of r.v using three set of parameters rather than two. The new model Frechet p.d.f is obtained and also its Cumulative distribution function is found then we apply three methods of estimation (which are Maximum likelihood , moments estimator , and the third method is depend on using least square regression approach). Different set of initial values of parameters ( , , ) and different samples size (n=25,50,75,100). The simulation procedure is done using matlab-R2014b, and results are compared using integrated Mean square error.

scholarly journals Recurrence of extreme observations

1959 ◽  
Vol 1 (1) ◽  
pp. 106-112 ◽  
Author(s):  
S. S. Wilks
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Independent Observations

Suppose a preliminary set of m independent observations are drawn from a population in which a random variable x has a continuous but unknown cumulative distribution function F(x). Let y be the largest observation in this preliminary sample. Now suppose further observations are drawn one at a time from this population until an observation exceeding y is obtained. Let n be the number of further drawings required to achieve this objective. The problem is to determine the distribution function of the random variable n. More generally, suppose y is the r-th from the largest observation in the preliminary sample and let n denote the number of further trials required in order to obtain k observations which exceed y. What is the distribution function of n?

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