In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which asserts uniform convergence of the empirical Cumulative Distribution Function (CDF) to the CDF of the underlying distribution. Our variant allows for tighter convergence bounds for extreme values of the CDF. We apply our bound in the context of revenue learning, which is a well-studied problem in economics and algo...

Outliers are observations that significantly different from the other in a dataset. These types of asymmetric nature due to lack symmetry. The estimation cumulative distribution function (CDF) is an important statistical measure commonly discussed for symmetric datasets. However, CDF case dataset not much-explored topic. In this article, we use calibration methodology with auxiliary information...

b a c k g r o u n d & aim: in many studies, the survival of patients with chronic kidney disease who are treated with peritoneal dialysis technique has been considered, while this is possible in peritoneal dialysis  patients  to switch  to another  treatment.  to achieve  more  accurate  estimation  of patient survival is necessary to examine all events. the purpose of this study is to estimate...

In this paper, considering dual-hop channel state information (CSI)-assisted amplify-and-forward (AF) relaying over Nakagami-m fading channels, the cumulative distribution function (CDF) of the endto-end signal-to-noise ratio (SNR) is derived. In particular, when the fading shape factors m1 and m2 at consecutive hops take non-integer values, the bivariate H-function and G-function are exploited...

This paper presents an investigation of approaches to modeling lower and upper subjective probabilities. A relatively unexplored approach is introduced, based on the fact that every cumulative distribution function (CDF) with support (0,1) has a “dual” CDF that obeys the conjugacy relation between coherent lower and upper probabilities. A new 2-parameter family of “CDF-Quantile” distributions w...

In this paper, we show that the covariance-eigenvalue approach converges much faster than using cumulative distribution function (CDF) for determining diversity gain from channel measurements in reverberation chamber. The covariance-eigenvalue approach can be used for arbitrary multi-port antennas, but it is limited to Maximum Ratio Combining (MRC). key words: MRC, diversity gain, eigenvalue, r...

Abstract Let $q\ge2$ be an integer, $\{X_n\}_{n\geq 1}$ a stochastic process with state space $\{0,\ldots,q-1\}$ , and F the cumulative distribution function (CDF) of $\sum_{n=1}^\infty X_n q^{-n}$ . We show that stationarity is equivalent to functional equation obeyed by use this characterize characteristic X structure in terms its Lebesgue decomposition. More precisely, while absolutely conti...

This paper presents analytical solutions for the performance of a single relay aided amplify-and-forward (AF) direct sequence code division multiple access (DS-CDMA) system over Rayleigh/Nakagami-m fading channels. The source-destination channel is assumed to be Rayleigh distributed while relay-destination link is Nakagami-m distributed. First, a cumulative distribution function (CDF) is derive...

Spectrum-sharing backscatter communication (SSBC) systems are among the most prominent technologies for ultralow power and spectrum-efficient communications. In this article, we propose an underlay SSBC system, in which secondary network is a system. We analyze performance of under transmit adaption strategy at transmitter, guarantees that interference caused by to primary receiver below predet...

Given a random variable X, we de ne a cumulative distribution function (cdf), FX : R → [0, 1], such that FX(t) = P{X ≤ t} for all t ∈ R. Here P{X ≤ t} denotes the probability that X ≤ t. To emphasize that random variable X has cdf FX , we write X ∼ FX . Note that FX(t) is a nondecreasing function of t. There are 3 types of random variables: discrete, continuous, and mixed. Discrete random varia...