scholarly journals Weak convergence of product of sums of independent variables with missing values

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 73-81
Author(s):  
Ivana Ilic
Keyword(s):  
Weak Convergence ◽  
Missing Values ◽  
Random Variables ◽  
Independent Variables ◽  
Products Of Sums ◽  
Incomplete Sample

Let (Xn) be a sequence of independent and non-identically distributed random variables. We assume that only observations of (Xn) at certain points are available. We study limit properties in the sense of weak convergence in the space D[0,1] of certain processes based on an incomplete sample from {X1, X2 ...,Xn }. This is an extension of the results of Matula and Stepien [2009. Weak convergence of products of sums of independent and non-identically distributed random variables. J. Math. Anal. Appl. 353, 49-54].

scholarly journals Functional Limit Theorem for Products of Sums of Independent and Nonidentically Distributed Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Przemysław Matuła ◽  
Iwona Stępień
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Limit Theorems ◽  
Random Variables ◽  
Functional Limit Theorem ◽  
Functional Limit ◽  
Generalize Limit ◽  
Products Of Sums

We study the weak convergence in the spaceD[0,1]of processes constructed from products of sums of independent but not necessarily identically distributed random variables. The presented results extend and generalize limit theorems known so far for i.i.d. sequences.

scholarly journals Weak and Almost Sure Convergence for Products of Sums of Associated Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Przemyslaw Matula ◽  
Iwona Stepien
Keyword(s):  
Weak Convergence ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Stationary Sequences ◽  
Associated Random Variables ◽  
Products Of Sums ◽  
Normal Law ◽  
Log Normal

We study weak convergence of product of sums of stationary sequences of associated random variables to the log-normal law. The almost sure version of this result is also presented. The obtained theorems extend and generalize some of the results known so far for independent or associated random variables.

scholarly journals A Simple Method for Converting 1-km Resolution Daily Clear-Sky LST into Real LST

2020 ◽  
Vol 12 (10) ◽  
pp. 1641
Author(s):  
Yunfei Zhang ◽  
Yunhao Chen ◽  
Jing Li ◽  
Xi Chen
Keyword(s):  
Land Surface ◽  
Missing Values ◽  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Shortwave Radiation ◽  
Simple Method ◽  
The Real ◽  
Independent Variables ◽  
Clear Sky ◽  
Reconstruction Methods

Land-surface temperature (LST) plays a key role in the physical processes of surface energy and water balance from local through global scales. The widely used one kilometre resolution daily Moderate Resolution Imaging Spectroradiometer (MODIS) LST product has missing values due to the influence of clouds. Therefore, a large number of clear-sky LST reconstruction methods have been developed to obtain spatially continuous LST datasets. However, the clear-sky LST is a theoretical value that is often an overestimate of the real value. In fact, the real LST (also known as cloudy-sky LST) is more necessary and more widely used. The existing cloudy-sky LST algorithms are usually somewhat complicated, and the accuracy needs to be improved. It is necessary to convert the clear-sky LST obtained by the currently better-developed methods into cloudy-sky LST. We took the clear-sky LST, cloud-cover duration, downward shortwave radiation, albedo and normalized difference vegetation index (NDVI) as five independent variables and the real LST at the ground stations as the dependent variable to perform multiple linear regression. The mean absolute error (MAE) of the cloudy-sky LST retrieved by this method ranged from 3.5–3.9 K. We further analyzed different cases of the method, and the results suggested that this method has good flexibility. When we chose fewer independent variables, different clear-sky algorithms, or different regression tools, we also achieved good results. In addition, the method calculation process was relatively simple and can be applied to other research areas. This study preliminarily explored the influencing factors of the real LST and can provide a possible option for researchers who want to obtain cloudy-sky LST through clear-sky LST, that is, a convenient conversion method. This article lays the foundation for subsequent research in various fields that require real LST.

scholarly journals Asymptotics for self-normalized random products of sums of i.i.d. random variables

2007 ◽  
Vol 334 (2) ◽  
pp. 1246-1259 ◽  
Author(s):  
Tian-Xiao Pang ◽  
Zheng-Yan Lin ◽  
Kyo-Shin Hwang
Keyword(s):  
Random Variables ◽  
Products Of Sums ◽  
Random Products

Distances on circles, toruses and spheres

1978 ◽  
Vol 15 (1) ◽  
pp. 136-143 ◽  
Author(s):  
B. W. Silverman
Keyword(s):  
Weak Convergence ◽  
Empirical Distribution ◽  
Random Variables ◽  
Suitable Function ◽  
Distribution Process

Families of heavily dissociated random variables are defined and discussed. These include families of the form g(Yi, Yj) for some suitable function g of two arguments and independent uniformly distributed random variables Y1, Y2, ··· on the circle, the torus or the sphere. The weak convergence of the empirical distribution process is discussed. The particular case of distances between pairs of observations on the circle is considered in greater detail.

Some Functional Stable Limit Theorems

1973 ◽  
Vol 16 (2) ◽  
pp. 173-177 ◽  
Author(s):  
D. R. Beuerman
Keyword(s):  
Weak Convergence ◽  
Limit Theorems ◽  
Stable Process ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Stable Limit ◽  
Stable Law ◽  
Partial Sum Process ◽  
Image Position

Let Xl,X2,X3, … be a sequence of independent and identically distributed (i.i.d.) random variables which belong to the domain of attraction of a stable law of index α≠1. That is,1whereandwhere L(n) is a function of slow variation; also take S0=0, B0=l.In §2, we are concerned with the weak convergence of the partial sum process to a stable process and the question of centering for stable laws and drift for stable processes.

scholarly journals Analysis of the Effects of High Precipitation in Texas on Rainfed Sorghum Yields

Water ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1920 ◽  
Author(s):  
Sharma ◽  
Kannan ◽  
Cook ◽  
Pokhrel ◽  
McKenzie
Keyword(s):  
Crop Yield ◽  
Missing Values ◽  
Crop Yields ◽  
Principal Component ◽  
Growing Season ◽  
Grain Sorghum ◽  
Extreme Weather Events ◽  
Total Precipitation ◽  
Independent Variables ◽  
Two Parameters

Most of the recent studies on the consequences of extreme weather events on crop yields are focused on droughts and warming climate. The knowledge of the consequences of excess precipitation on the crop yield is lacking. We attempted to fill this gap by estimating reductions in rainfed grain sorghum yields for excess precipitation. The historical grain sorghum yield and corresponding historical precipitation data are collected by county. These data are sorted based on length of the record and missing values and arranged for the period 1973–2003. Grain sorghum growing periods in the different parts of Texas is estimated based on the east-west precipitation gradient, north-south temperature gradient, and typical planting and harvesting dates in Texas. We estimated the growing season total precipitation and maximum 4-day total precipitation for each county growing rainfed grain sorghum. These two parameters were used as independent variables, and crop yields of sorghum was used as the dependent variable. We tried to find the relationships between excess precipitation and decreases in crop yields using both graphical and mathematical relationships. The result were analyzed in four different levels; 1. Storm by storm consequences on the crop yield; 2. Growing season total precipitation and crop yield; 3. Maximum 4-day precipitation and crop yield; and 4. Multiple linear regression of independent variables with and without a principal component analysis (to remove the correlations between independent variables) and the dependent variable. The graphical and mathematical results show decreases in rainfed sorghum yields in Texas for excess precipitation could be between 18% and 38%.

Limit theorems for dissociated random variables

1976 ◽  
Vol 8 (04) ◽  
pp. 806-819 ◽  
Author(s):  
B. W. Silverman
Keyword(s):  
Data Analysis ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Weak Convergence ◽  
Limit Theorems ◽  
Normal Approximation ◽  
Empirical Distribution ◽  
Random Variables ◽  
Distribution Process ◽  
Suitable Space

Families of exchangeably dissociated random variables are defined and discussed. These include families of the form g(Yi, Yj , …, Yz ) for some function g of m arguments and some sequence Yn of i.i.d. random variables on any suitable space. A central limit theorem for exchangeably dissociated random variables is proved and some remarks on the closeness of the normal approximation are made. The weak convergence of the empirical distribution process to a Gaussian process is proved. Some applications to data analysis are discussed.

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