• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.877-896
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• 2017

In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.57-72
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• 2016

We establish maximal moment inequalities of partial sums under ${\psi}$-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-342], to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with ${\psi}$-weakly dependent innovations.

• International Journal of Reliability and Applications
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• v.4 no.4
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• pp.191-199
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• 2003

In the present work, a moment inequality is derived for new renewal better (worse) than used in expectation(NRBUE) (NRWUE) distributions. This inequality demonstrates that if the mean life is finite then all higher order moments exist. A new test statistics for testing exponentiality against NRBUE (NRWUE) is introduced based on this inequality. It is shown that the proposed test is simple and has high relative efficiency for some commonly used alternatives. Critical values are tabulated for sample sizes n = 5(1)30. A set of real data is used as an example to elucidate the use of the proposed test statistics for practical reliability analysis.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.327-349
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• 2021

In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.

• International Journal of Reliability and Applications
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• v.5 no.4
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• pp.105-113
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• 2004

The exponential better (worse) than used EBU (EWU) class of life distributions is considered. A moment inequality is derived for EBU (EWU) distributions which demonstrate that if the mean life is finite, then all moments exist. Based on this inequality, a new test statistic for testing exponentiality against EBU (EWU) is introduced. It is shown that the proposed test is simple, enjoys good power and has high relative efficiency for some commonly used alternatives. Critical values are tabulated for sample sizes n = 5(1)40. A set of real data is used as a practical application of the proposed test in the medical science.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.209-213
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• 2002

We study maximal second moment inequality and derive complete convergence for weighted sums of asymptotically almost negatively associated(AANA) random variables by applying this inequality. 2000 Mathematics Subject Classification : 60F05

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.491-506
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• 2019

In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.5
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• pp.111-118
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• 2020

This paper examines the impacts of credit on income inequality in Vietnam. Though it is one of the most common measures of financial development, there is a dearth of research in this area. Unlike previous studies, the paper disaggregates the impact of each type of credit on income inequality, looking at the Gini coefficient. We employ the Generalized Method of Moment (GMM) to solve the endogenous problem. The primary data set contains a panel of 60 Provincial observations, from data collected from the General Statistics Office of Vietnam from 2002 to 2016. The empirical findings show that, while commercial credit increases income inequality, policy credit contributes to reducing income inequality in Vietnam. The results also confirm the important roles of education, institutional quality and foreign direct investment in fighting against income inequality in Vietnam. However, the paper does not provide adequate evidence to support the inverted U-shaped relationship between credit and income inequality. Based on the findings, we argue that the government should direct flows of credit to real economic activities rather than speculative investment; more bank credit should be allocated to rural areas and agriculture; and favorable credit programs should be designed to promote education, especially of those living in rural areas.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.12
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• pp.19-29
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• 2021

This study aims to measure financial inclusion and examine its impact on income inequality in a panel of 18 Asian countries over the period 1997-2017. Two alternative approaches for developing financial inclusion index are used: one approach following the methodology of Sarma (2008), while the other is the Dynamic Factor Model (DFM)-based index. The impact of individual indicators and index of financial inclusion on inequality in income is analyzed. The Generalized Method of Moment (GMM) approach is used for empirical analysis. The results indicate that micro-level financial inclusion has a weak negative and statistically significant impact on income inequality. Macro-level index and all individual indicators of financial inclusion do not affect income inequality in the selected sample of economies. The income inequality issues have different natures and cannot be fixed by financial inclusion only. It needs holistic structural reforms to enable fair distribution of income and make an equitable financial system. Financial inclusion is a relatively less important intervention tool regarding fixing the issue of income inequality. This is one of the first studies that used the DFM method for financial inclusion indices construction.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1275-1292
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• 2016

The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to (0, ${\infty}$) instead of (0, 2), we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.