abstract

With the development of society, sports ability has also become an important item to evaluate a country's comprehensive ability. The London Olympic Games will open on July 27th, 20 12, and the Olympic medal list (the total number of gold, silver and copper) has become a hot issue that everyone cares about. I think the change of the number of Olympic medals is a Markov process, and based on this, a prediction model of the number of Olympic medals is established. When solving the transition probability matrix, we establish a programming model with the goal of minimizing the error between the predicted value and the actual value. With the help of Olympic medal data over the years, the optimal transfer probability matrix is obtained by LINGO software. Finally, it is substituted into the medal number prediction model, and it is concluded that the number of medals in China in the 30th Olympic Games is about 87. After adding the error term, the predicted number of medals is between 8 1-93. You can also reuse formula Y=? 1? 1+? 2? 2+? 3? 3+? +Simulate and predict the number of medals in each country this year.

Key words: medal number prediction, solution of transfer probability matrix P, host country effect, horse chain model, 1. Restatement of the problem

The London Olympic Games will open on July 27th, 20 12, and the Olympic medal list (the total number of gold, silver and bronze) has become a hot spot.

The problem is based on the previous medal rankings of various countries, as well as the various influences of economic development, population composition and government policies of various countries.

To the medal list, establish a mathematical model to predict the top five medals of the 20 12 London Olympic Games.

Second, the symbol description

x0

: the percentage of gold medals won by the host country in this Olympic Games to the total number of gold medals in this Olympic Games;

X: the average number of gold medals won by the host in other sessions as a percentage of the total number of gold medals in that session;

y0

: the percentage of medals won by the host country in this Olympic Games to the total number of medals won in this Olympic Games;

Y: the average percentage of medals won by the host country in other sessions to the total number of medals in that session;

N: The total number of Olympic gold medals won by this country.

I: country or region code (1, 2, 10)

T: Session number (1, 2,? 7)

Ni(t): The number of medals won by a country or region in which Olympic Games.

N (t): The total number of medals in the T Olympic Games.

Wi(t): The proportion of medals won in the first session of a country or region to the total.

W(t): the structural vector of the number of T medals in each country or region.

P, pij: transition probability matrix, transition probability matrix elements

Vi(t): the proportional error of the number of medals.

Third, the model hypothesis.

(1) Assume that the sports strength of other countries has not changed much;

(2) Assuming that the 30th Olympic Games is held as scheduled, the number of medals in various countries is not affected by the date; (3) Suppose London Olympic Games

The number of medals established shall not be less than that of previous Olympic Games;

(4) Assume that the number of Olympic medals in each country has no aftereffect, that is, the winning situation is only related to the winning situation in the previous session.

(5) Suppose that the main influencing events of the Olympic Games are track and field, while swimming and gymnastics are the secondary influencing factors.

(6) It is assumed that Olympic athletes from all countries play normally.

(7) Not considering the influence of political factors on participating countries;

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