A new family of multivariate slash distributions

In this article, a new form of multivariate slash distribution is introduced and some statistical properties are derived. In order to illustrate the advantage of this distribution over the existing generalized multivariate slash distribution in the literature, it is applied to a real data set.     

Coining societies: an inter-functional comparative analysis of the Euro

The present analysis of the Euro looks for the marks that function systems make on what we commonly take for the European money. Clearly distinguishing between coins and currency, the Euro coins and banknotes are not taken for economic tokens per se but for storage devices that contain both economic and noneconomic information. A systemic analysis of the function system references on these storage devices shows that the economy has left fewer marks on the Euro than politics, art, and the mass media systems have. We, hence, argue that “the Euro” “is” not just money with a political second mission but rather can be understood as an indicator of the relative relevance that specific function systems do or do not have for the European societies and the European society.     

Moment‐Independent Sensitivity Analysis Using Copula

In risk assessment, the moment‐independent sensitivity analysis (SA) technique for reducing the model uncertainty has attracted a great deal of attention from analysts and practitioners. It aims at measuring the relative importance of an individual input, or a set of inputs, in determining the uncertainty of model output by looking at the entire distribution range of model output. In this article, along the lines of Plischke et al., we point out that the original moment‐independent SA index (also called delta index) can also be interpreted as the dependence measure between model output and input variables, and introduce another moment‐independent SA index (called extended delta index) based on copula. Then, nonparametric methods for estimating the delta and extended delta indices are proposed. Both methods need only a set of samples to compute all the indices; thus, they conquer the problem of the “curse of dimensionality.” At last, an analytical test example, a risk assessment model, and the levelE model are employed for comparing the delta and the extended delta indices and testing the two calculation methods. Results show that the delta and the extended delta indices produce the same importance ranking in these three test examples. It is also shown that these two proposed calculation methods dramatically reduce the computational burden.     

Optimal split‐plot orthogonal arrays

It is well known that many industrial experiments have split‐plot structures. Compared to completely randomised experiments, split‐plot designs are more economical and thus have received much attention among researchers. Much work has been done for two‐level split‐plot designs. In this article, we consider split‐plot designs with factors of three, more than three, or mixed levels and with both qualitative and quantitative factors. We show that if two designs with both qualitative and quantitative factors are geometrically isomorphic, then their generalised wordlength patterns are identical. Three design scenarios are considered for optimal designs. The corresponding wordlength patterns are defined and the minimum aberration mixed‐level split‐plot designs having 18 and 36 runs are tabulated.     

Empirical Uncertain Bayes Methods in Area‐level Models

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area‐level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an estimation error. Thus, it is desirable to consider the uncertain prior distribution, which is expressed as the mixture of a one‐point distribution and a proper prior distribution. In this paper, we develop an empirical Bayes approach for estimating area‐level means, using the uncertain prior distribution in the context of a natural exponential family, which we call the empirical uncertain Bayes (EUB) method. The regression model considered in this paper includes the Poisson‐gamma and the binomial‐beta, and the normal‐normal (Fay–Herriot) model, which are typically used in small area estimation. We obtain the estimators of hyperparameters based on the marginal likelihood by using a well‐known expectation‐maximization algorithm and propose the EUB estimators of area means. For risk evaluation of the EUB estimator, we derive a second‐order unbiased estimator of a conditional mean squared error by using some techniques of numerical calculation. Through simulation studies and real data applications, we evaluate a performance of the EUB estimator and compare it with the usual empirical Bayes estimator.     

Statistical analysis of dependent competing risks model in accelerated life testing under progressively hybrid censoring using copula function

This article considers statistical analysis of dependent competing risks model from Weibull distribution in accelerated life testing, in which copula function is used to examine the dependence structure between competing failure modes. We derive the maximum likelihood estimates, the approximate, and Bootstrap confidence intervals of the parameters. The effects of different dependence structures on the estimates of parameters are investigated. The simulation is given to compare the performance of the estimates when the competing failure modes are dependent with those when the failure modes are independent. Finally, one dataset was used for illustrative purpose in conclusion.     

Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes

We consider spatial point processes with a pair correlation function, which depends only on the lag vector between a pair of points. Our interest is in statistical models with a special kind of ‘structured’ anisotropy: the pair correlation function is geometric anisotropic if it is elliptical but not spherical. In particular, we study Cox process models with an elliptical pair correlation function, including shot noise Cox processes and log Gaussian Cox processes, and we develop estimation procedures using summary statistics and Bayesian methods. Our methodology is illustrated on real and synthetic datasets of spatial point patterns.     

Tests for Structural Changes in Time Series of Counts

We propose methods for detecting structural changes in time series with discrete‐valued observations. The detector statistics come in familiar L2‐type formulations incorporating the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. For both models, we study mainly structural changes due to a change in distribution, but we also comment for the classical problem of parameter change. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is also included along with a real data example.     

韩国全罗南道岁时风俗研究

Seasonal customs, also called“performances that take place within a one year cycle”, refer to a series of customs, patterns or norms practiced periodically and habitually on spe-cific days within the regular cycle of the four sea-sons. Seasonal customs are found in every month, such as the Spring Festival in the first month, Laborers’ Day in the second month, The 3rd day in the third month, the birthday of Sakyamuni in the fourth month, the Dano Festival in the fifth month, etc. ( all dates mentioned in this paper are in the lunar calendar) . As the years go by, the seasonal customs change constantly. Many of them have been faded as society has changed, and they have been replaced by National Holidays or other legal holidays which regulate people’s lives. In addition, as western and other cultures filter in, holidays like Valentine’s Day, and Christmas have stepped into people’s lives. Because these festivals are no longer linked with traditional religious meanings found in the old customs, and place more emphasis on entertainment, they have been accepted almost instantly, taking up social space, and changing people’s activities and behaviors. Apart from these, festivals in some particular areas became popular and spread nationwide as the result of na-tional policies. As an important constituent, seasonal customs can reveal the cultural state and spiritual world of a country or region. Jeollanam-do in South Korea, known as the treasure house of customs, possesses rich customs and heritage and various annual cus-toms can be seen here. This paper, by making a general investigation of the customs in Jeollanam-do, can help us further understand the state of this region’s history and ideology, and the cultural im-plications hidden within it. In the first month of the lunar calendar, the primary festivals are the Spring Festival, the First Day of the First Lunar Month, and the Fifteenth Day of the First Lunar Month. 1 ) In the Spring Festival, the most important activities are offering sacrifices to gods and ancestors, sweeping tombs, and paying New Year’s visits. People also believe that this is the proper time to avoid the“three dis-asters”, keep away night ghosts, burn hair, and go to fortune tellers, etc. There are also games played in this period, such as the see-saw and board-turning. 2) the First Day of the First Lunar Month cannot be counted as a traditional festival. However, a day’s rest is taken in the countryside when every house sticks spring couplets on their doors or pillars. These are pairs of long strips of paper on which auspicious words or sayings are written. 3 ) In traditional society, when farming dominated, people observed the Fifteenth Day of the First Lunar Month with grand ceremony, main-ly through engaging in entertaining activities. In Jeollanam-do, the festival atmosphere is warmly created by playing folk or peasant music, flying kites, playing tug-of-war games, or Gohssaum, and so on. In addition to the group activities, indi-vidual families might offer sacrifices in their hou-ses. Each village also offers sacrifices together, known as the Tangshan Sacrifice and Dragon King Sacrifice. There are various superstitions related to this day. For example, many people will buy a strainer and hang it at home, believing that it will bring blessings. Or, on the eve of this day people might set fires on field ridges, believing that this will bring a good harvest. People might also set up Changsheng or Changganzi, along the borders or milestones separating villages from each other, which are known as the patron gods protecting their territory. On this day the staple food is supposed to be“Wugufan”, literally“Rice with Five Grains”, which actually includes more than five kinds of va-rious grains. It is so-called because all the main grains are collectively called “five grains”. In ad-dition, people also cook the“Eight Treasures Rice Soup” which contains glutinous rice, Chinese dates, chestnut, honey, pine nuts, an beans, etc. In the second lunar month, there are the Laborers’ Day and the Yongdung Festival. On the 1st of the second month, Laborers’ Day, laborers used to be given a day’s rest when people made a kind of dessert known as “Agecake”. However, because no one hires laborers nowadays, this cus-tom has actually disappeared. It is said that on 1st day of the second month, Yongdung Halmoni de-scends from the sky, and returns there on the 15th or 20th day. Yongdung Halmoni is said to be the goddess in charge of wind, so, in fishing areas where wind matters a lot, people will offer sacri-fices to her. It is said that if Yongdung Halmoni descends with her daughter-in-law, the wind throughout the whole year will be too strong to guarantee a good harvest, but good sailings can be counted on if she descends with her daughter. On the 3rd day of the third month, women in Jeollanam-do bring simple cooking equipment to the riverside, and pass a pleasant day there. They mix glutinous rice powder with rhododendron petals to make pancakes which they call “flower pan-cakes”. While they eat, they sing songs about flower pancakes or other folk songs. Around 3 rd day of the third month, butterflies start to appear and “dance”. It is believed that if yellow butter-flies are seen first, the coming year will be smooth, but if white butterflies are seen first, there will be many funerals or other inauspicious things. On the 8 th day of the fourth month the birthday of Sakyamuni, many people go to the temples and hang Buddhist lanterns. The display of lanterns on that day is truly grand. It is attended mainly by women who pray for happiness, safety, good health, success and prosperity for their family members. In the temples, people perform the ritu-al of“circumambulating the stupas”, spending the entire night sleepless walking around the stupas, praising gods’ merits and credits, and repeating their wishes in their hearts. While circling the stu-pas, people usually listen to Buddhist chants,some places may play the traditional music with tradi-fional instrument. On the 5th day of the fifth month, on the Dano Festival, the following activities are found in Jeol-lanam-do. 1 ) wrestling, a competitive game played mainly by males; 2 ) swinging, played mainly by females; 3 ) washing hair with acorus calamus. It is believed that hair becomes smooth and shiny if washed with water boiled with acorus calamus. Therefore, many women wash their hair in this way on the 5th day of the fifth month. 4) imbibing herbal medicine. During the Dano Festi-val, all things on the earth are said to be suitable for medicine. There are drinkable herbal juices made from Leonurus heterophyllus, or Ay Tsao. People pluck all kinds of herbs and dry them for future use. The 15 th day of the sixth lunar month is Yudu Day. It is believed that if you wash your hair with clear stream water on this day, bad luck is kept a-way and you will not suffer heatstroke in summer. According to local folklore, the Dragon God and God of the field ditches check on the crops on this day, so no fieldwork is allowed, and a day’s rest is required. If people insist on going to work, it is said they will not have a good harvest. Rice cakes are also prepared on this day and placed in the crop fields as simple offerings to the Dragon God for a good harvest. In June, which has the hottest days in the year, the month is divided into the ini-tial, middle and final hottest days. In order to build up their health, people cook delicious gin-seng chicken soup by putting ginseng, jujubes and glutinous rice into the chicken’s abdomen. Or, for the sake of vitality, some men may drink a body-protecting soup, the so-called dog meat soup. The 7 th day of the seventh month is the Chilseok Festival. Since Chilseok is closely con-nected with the Chilseok God, every family will pray to the Chilseok God for blessings, or go to temples to offer sacrifices. In this festival some families may offer sacrifices to Chengzhu God as in other festivals, but not many offerings are required except for some rice and vegetable dishes. On the 15th day, the Baekjung Day, all kinds of fortune-telling activities prevail. All fieldwork stops and a day’s rest is taken. On this day people also prepare food to offer to the ancestors. The 15th day of the eight month, the Mid-Au-tumn Festival, is characterized by harvest and thanks-giving. Various activities can be seen in Je-ollanam-do, among which offering sacrifices and sweeping tombs are given priority, even more than during the Spring Festival. During the mid-autumn days everyone, rich or poor, makes Songbing, which is very much like a Chinese moon cake, and it is still the most representative festival food for the Mid-Autumn Festival Day. After finishing mak-ing the Songbing with newly harvested rice, people will carry them together with many fruits to offer sacrifices in the early morning and sweep tombs. Some people may go to the cemetery to pull weeds before sweeping tombs. At night, during the full moon, in order to liven up atmosphere, women will perform traditional dance . There is also a custom observed on the Mid-autumn day—married daugh-ters will meet with their own parents and relatives in a place located mid-way between the two homes. Sometimes, female neighbors may agree to meet with each other at a certain appointed place and bring food along to spend a pleasant day to-gether. The 9 th day of the ninth month is the Jungu Festival. It is no longer regarded as a particular festival, but it is still considered a lucky day. In the past, on this day, people would make wine, rice cakes and even medicine, out of chrysanthe-mums. Moreover, literati would appreciate poems as well as maple leaves, which were quite scenic. There are no special festivals during the 10 th lunar month, though this is considered a lucky month because many things forbidden in other months are permissible during this month. The 15th day is a day for some families to offer sacrifices to ancestors or drive away disasters. In rural areas, one of the family customs is for women to bathe and change their clothes before replacing the old rice in ancestor pot with newly harvested rice. This is re-garded as a recommended ritual to domestic gods of new rice. In the 11th lunar month, at the winter sol-stice, it is customary to have red bean soup, which is cooked with glutinous rice powder and red beans mixed together. Its red color is believed to protect people against evil spirits. People offer the red bean soup to their ancestors, and, splash it in front of doors, on walls, around the kitchen, and in their yards. This is all done in order to keep ghosts outside. The 30th day of the 12th month, New Year’s Eve, is the time to stay up late to see in the New Year. So, every house has lights on overnight. It is customary to visit elderly people and inquire a-bout their physical condition and to show care on this eve. This is called “paying an old year’s call”. In olden times, snow which fell in the 12 th month was put into bottles, and when the snow melted the water was believed to be a good medi-cine for curing heatstroke in summer. To sum up, seasonal customs in Jeollanam-do are multi-functional, including the following five aspects:1 ) worshipping the ancestors;2 ) praying for a good harvest and good fishing;3 ) keeping a-way bad luck and calling for blessings;4 ) sharing happiness and improving harmony;5 ) hygiene and health care. Folk customs in Jeollanam-do are diversified. While taken as the concrete outward representa-tions of seasonal customs, these folk scenarios car-ry distinctive features of local customs: 1 ) rural music is the most important factor constituting these seasonal customs by enriching the functions and connotations; 2 ) With its keen local charac-teristics, distinctive quality of including spells, and carrying a religious sensibility, games are part and parcel to seasonal customs; 3 ) Different cul-tural circles are accompanied by different customs and habits. So there are differences between inland and coastal or island areas, and even within the coastal area, differences can occur among particu-lar sea areas.