scholarly journals A method of value measurement based on conditional probability theory in economics

2021 ◽  
Author(s):  
Gang Xi ◽  
Xiaoyi Yang ◽  
Ming Xi
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Weighted Average ◽  
Random Variable ◽  
Conditional Probability Distribution ◽  
Mean And Variance ◽  
The Mean ◽  
New Perspective ◽  
Value Measurement ◽  
Quantitative Statistics

Abstract Value is one of the most fundamental concepts in economics. The existing main definitions of value have certain limitations and are difficult to be unified and quantified. Thus, this article presents a method of quantifying value based on the conditional probability theory; we set value as a random variable, a price is the value of the good in terms of money, according to the price’s historical records, quantitative statistics and human experiences, and thus uses conditional probability distribution to measure value. Furthermore, the mean and variance of random variables are used to describe the weighted average of the possible values and the dispersion of values distribution. This method provides a new perspective for the measurement of value.

scholarly journals A method of value measurement based on probability theory in economics

2021 ◽  
Author(s):  
Gang Xi ◽  
Xiaoyi Yang ◽  
Ming Xi
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Weighted Average ◽  
Random Variable ◽  
Conditional Probability Distribution ◽  
Mean And Variance ◽  
The Mean ◽  
New Perspective ◽  
Value Measurement ◽  
Quantitative Statistics

Abstract Value is one of the most fundamental concepts in economics. The existing main definitions of value have certain limitations and are difficult to be unified and quantified. Thus, this article presents a method of quantifying value based on the conditional probability theory; we set value as a random variable, a price is the value of the good in terms of money, according to the price’s historical records, quantitative statistics and human experiences, and thus uses conditional probability distribution to measure value. Furthermore, the mean and variance of random variables are used to describe the weighted average of the possible values and the dispersion of values distribution. This method provides a new perspective for the measurement of value.

scholarly journals A method of value measurement based on conditional probability theory

2020 ◽  
Author(s):  
Gang Xi ◽  
Xiaoyi Yang ◽  
Ming Xi
Keyword(s):  
Probability Theory ◽  
Conditional Probability ◽  
Weighted Average ◽  
Random Variable ◽  
Conditional Probability Distribution ◽  
Mean And Variance ◽  
The Mean ◽  
New Perspective ◽  
Value Measurement ◽  
Values Distribution

Abstract Value is one of the most fundamental concepts in economics. The existing main definitions of value have certain limitations and are difficult to be unified and quantified. Thus, this article presents a method of quantifying value based on the conditional probability theory; we set value as a random variable, and thus uses conditional probability distribution to measure value. Furthermore, the mean and variance of random variables are used to describe the weighted average of the possible values and the dispersion of values distribution. This method provides a new perspective for the measurement of value.

Asymptotic properties of the number of replications of a paired comparison

1974 ◽  
Vol 11 (1) ◽  
pp. 43-52 ◽  
Author(s):  
V. R. R. Uppuluri ◽  
W. J. Blot
Keyword(s):  
Paired Comparison ◽  
Beta Function ◽  
Asymptotic Properties ◽  
Random Variable ◽  
Incomplete Beta Function ◽  
Discrete Random Variable ◽  
World Series ◽  
Mean And Variance ◽  
The Mean ◽  
Made In

A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta function with equal arguments is obtained. This expression is used in deriving asymptotic (m-large) expressions for the mean and variance. The standardized variate is shown to converge to the Gaussian distribution as m→ ∞. A result corresponding to the DeMoivre-Laplace limit theorem is proved. Finally applications are made to the genetic code problem, to Banach's Match Box Problem, and to the World Series of baseball.

The Largest Missing Value in a Sample of Geometric Random Variables

2014 ◽  
Vol 23 (5) ◽  
pp. 670-685 ◽  
Author(s):  
MARGARET ARCHIBALD ◽  
ARNOLD KNOPFMACHER
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Missing Value ◽  
Asymptotic Expressions ◽  
Mean And Variance ◽  
The Mean ◽  
Special Case

We consider samples of n geometric random variables with parameter 0 < p < 1, and study the largest missing value, that is, the highest value of such a random variable, less than the maximum, that does not appear in the sample. Asymptotic expressions for the mean and variance for this quantity are presented. We also consider samples with the property that the largest missing value and the largest value which does appear differ by exactly one, and call this the LMV property. We find the probability that a sample of n variables has the LMV property, as well as the mean for the average largest value in samples with this property. The simpler special case of p = 1/2 has previously been studied, and verifying that the results of the present paper coincide with those previously found for p = 1/2 leads to some interesting identities.

scholarly journals Not all females outlive all males: A new perspective on lifespan inequalities between sexes

2020 ◽  
Author(s):  
Marie-Pier Bergeron-Boucher ◽  
Jesús-Adrian Alvarez ◽  
Ilya Kashnitsky ◽  
Virginia Zarulli ◽  
James W Vaupel
Keyword(s):  
Life Expectancy ◽  
18Th Century ◽  
Combined Effect ◽  
Summary Statistics ◽  
Suggested Approach ◽  
Death Rates ◽  
Mean And Variance ◽  
The Mean ◽  
New Perspective

Differences in lifespan between populations, e.g. between females and males, are often measured by differences in summary statistics, such as life expectancy, which generally show an advantage of females over males across the whole age span. However, such statistics ignore the fact that two lifespan distributions are generally not mutually exclusive and that not all females outlive all males. Here we use a novel measure of inequality in lifespans: the outsurvival probability, which is interpreted as the probability of males to outlive females. The measure accounts for the similarities in lifespan between populations. It also considers the interaction between the mean and variance of two lifespan distributions and their combined effect on between-populations inequalities. Our results show that the probability of males outliving females varied between 25% and 50%, across 44 countries and regions since the middle of the 18th century. Thus, despite the usually male lower life expectancy and higher death rates at all ages, males have a substantial chance of outliving females. Our suggested approach is generalizable to any pair of populations.

STATISTICAL INFERENCE FOR K INDEPENDENT, HOMOGENEOUS ARITHMETIC PROCESSES

2000 ◽  
Vol 07 (03) ◽  
pp. 223-236 ◽  
Author(s):  
FRANCIS KIT-NAM LEUNG
Keyword(s):  
Stochastic Process ◽  
Linear Regression ◽  
Renewal Process ◽  
Random Variable ◽  
Simple Linear Regression ◽  
Variable Formula ◽  
Mean And Variance ◽  
The Mean ◽  
Time Continuum ◽  
Area Of Application

For k=1,…, K, a stochastic process {An,k, n =1, 2,…} is an arithmetic process (AP) if there exists some real number, d, so that {An,k +(n-1)d, n =1, 2,…} is a renewal process (RP). AP is a stochastically monotonic process and can be used to model a point process, i.e., point events occurring in a haphazard way in time (or space), especially with a trend. For example, the events may be failures arising from a deteriorating machine; and such a series of failures is distributed haphazardly along a time continuum. In this paper, we discuss estimation procedures for K independent, homogeneous APs. Two statistics are suggested for testing whether K given processes come from a common AP. If this is so, we can estimate the parameters d, [Formula: see text] and [Formula: see text] of the AP based on the techniques of simple linear regression, where [Formula: see text] and [Formula: see text] are the mean and variance of the first average random variable [Formula: see text], respectively. In this paper, the procedures are, for the most part, discussed in reliability terminology. Of course, the methods are valid in any area of application, in which case they should be interpreted accordingly.

scholarly journals Estimation of Hazard Rate and Mean Residual Life Ordering for Fuzzy Random Variable

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
S. Ramasubramanian ◽  
P. Mahendran
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Mean Residual Life ◽  
Mean And Variance ◽  
The Mean ◽  
Hazard Rate Ordering ◽  
Fuzzy Random

L2-metric is used to find the distance between triangular fuzzy numbers. The mean and variance of a fuzzy random variable are also determined by this concept. The hazard rate is estimated and its relationship with mean residual life ordering of fuzzy random variable is investigated. Additionally, we have focused on deriving bivariate characterization of hazard rate ordering which explicitly involves pairwise interchange of two fuzzy random variablesXandY.

PREDICTING CONDITIONAL PROBABILITY DISTRIBUTIONS: A CONNECTIONIST APPROACH

1995 ◽  
Vol 06 (02) ◽  
pp. 109-118 ◽  
Author(s):  
ANDREAS S. WEIGEND ◽  
ASHOK N. SRIVASTAVA
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Conditional Probability ◽  
Nearest Neighbor ◽  
Single Point ◽  
Main Idea ◽  
Classification Problem ◽  
Conditional Probability Distribution ◽  
Regression Problem ◽  
The Mean

Most traditional prediction techniques deliver a single point, usually the mean of a probability distribution. For multimodal processes, instead of predicting the mean, it is important to predict the full distribution. This article presents a new connectionist method to predict the conditional probability distribution in response to an input. The main idea is to transform the problem from a regression problem to a classification problem. The conditional probability distribution network can perform both direct predictions and iterated predictions, the latter task being specific for time series problems. We compare this new method to fuzzy logic and discuss important differences, and also demonstrate the architecture on two time series. The first is the benchmark laser series used in the Santa Fe competition, a deterministic chaotic system. The second is a time series from a Markov process which exhibits structure on two time scales. The network produces multimodal predictions for this series. We compare the predictions of the network with a nearest-neighbor predictor and find that the conditional probability network is more than twice as likely a model.

scholarly journals Asymptotic Properties of a Leader Election Algorithm

2011 ◽  
Vol 48 (02) ◽  
pp. 569-575 ◽  
Author(s):  
Ravi Kalpathy ◽  
Hosam M. Mahmoud ◽  
Mark Daniel Ward
Keyword(s):  
Geometric Distribution ◽  
Asymptotic Properties ◽  
Random Variable ◽  
Leader Election ◽  
Wasserstein Metric ◽  
Coin Tossing ◽  
Mean And Variance ◽  
The Mean ◽  
Election Algorithm ◽  
Leader Election Algorithm

We consider a serialized coin-tossing leader election algorithm that proceeds in rounds until a winner is chosen, or all contestants are eliminated. The analysis allows for either biased or fair coins. We find the exact distribution for the duration of any fixed contestant; asymptotically, it turns out to be a geometric distribution. Rice's method (an analytic technique) shows that the moments of the duration contain oscillations, which we give explicitly for the mean and variance. We also use convergence in the Wasserstein metric space to show that the distribution of the total number of coin flips (among all participants), suitably normalized, approaches a normal limiting random variable.

Asymptotic properties of the number of replications of a paired comparison

1974 ◽  
Vol 11 (01) ◽  
pp. 43-52 ◽  
Author(s):  
V. R. R. Uppuluri ◽  
W. J. Blot
Keyword(s):  
Paired Comparison ◽  
Beta Function ◽  
Asymptotic Properties ◽  
Random Variable ◽  
Incomplete Beta Function ◽  
Discrete Random Variable ◽  
World Series ◽  
Mean And Variance ◽  
The Mean ◽  
Made In

A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta function with equal arguments is obtained. This expression is used in deriving asymptotic (m-large) expressions for the mean and variance. The standardized variate is shown to converge to the Gaussian distribution as m→ ∞. A result corresponding to the DeMoivre-Laplace limit theorem is proved. Finally applications are made to the genetic code problem, to Banach's Match Box Problem, and to the World Series of baseball.

Sign in / Sign up

Export Citation Format

Share Document