Application of mathematical probabilistic statistical model of base – FFCA financial data processing

At the same time, these models explore the internal law of the financial market, providing an efficient solution for managers and decision-makers in the financial market to improve the market economy system. The statistical model of real-world data usually involves continuous probability distribution, such as normal, Laplace, or index distribution. This distribution is supported by many probabilistic modeling forms, including probability database systems. However, the traditional theoretical framework of the probability database is completely concerned with the limited probability database [3]. Yue et al. [4] developed mathematical theories in unlimited probability databases. In a previous paper (GROHE, LINDNER; ICDT 2020), a very general framework is proposed for the probability database that may involve a continuous probability distribution; the query has a clear definition in this framework. Extending the probability programming language to generate data records (PODS 2020) to achieve a continuous probability distribution and displaying such programs generates a continuous probability database generation model [4]. Zhang [5] has developed a new way to have a nonprogrammetry of boundaries to accurately surround all uncertain parameter data extracted in the actual project. This method is based on conventional statistical methods and related analysis techniques. First, the average value and the correlation coefficient of the uncertain parameter are calculated by using all given data.

Then, first, a simple but effective optimization process is introduced in the mathematical modeling process to induce the uncertain parameters to obtain their exact boundaries. This process operates on all of the given data by optimizing the convex mode. Thus, an effective mathematical expression of the final formulation of the convex mode is obtained. In order to test the predictive capacity and generalization ability of the proposed convex mode, the evaluation criteria used are volume ratio, standard volume ratio, and prediction accuracy. The performance of the proposed method is studied by testing standards and comparing with other existing competition methods. The results prove the effectiveness and efficiency of the method [5]. Herrera-Vega et al. [6] propose a probabilistic hesitant financial data (PHFD)-based portfolio selection and risk portfolio selection model, i.e., probabilistic hesitant portfolio selection (PHPS) model and risk PHPS (RPHPS) model, of risk probability hesitation.

In addition, investment decision methods are provided to show their practical applications in the financial market. It is expected that the PHPS model of general investors is built based on the highest score or minimum deviation principle to obtain the best investment ratio, and the RPHPS model provides the best investment ratio for the best return or to undertake risk. Finally, an empirical study based on the actual data of China’s stock market is shown in detail. The results verify the effectiveness and practicality of the proposed method [6]. Li et al. used mathematical statistical methods to study the effectiveness of single-stage and multistage hydraulic fracturing technology. These studies are based on the geological and physical properties of the circulation of the prime wall, which makes it possible to demonstrate the choice of hydraulic fracturing technology.

Based on the probability and statistical analysis of the field efficiency data, quantitative standards selected by the crack parameters of propanes by length, height, and the injection of propane have been established. They can be used to predict the use of multistage and single-stage hydraulic fracturing methods. High-efficiency horizon AS12-3 has complex geological and physical structures and low filtering and storage performance, making it complicated, and contributes to the active formation of the reserves that are difficult to recover. Single-stage hydraulic fracturing technology is only 3–4 years old. Hydraulic fracturing technology with single-stage hydraulic fracturing technology is more effective [7].

The mathematical modeling analysis of data filtration is performed by the probability mathematical model. First, the sample descriptive statistical analysis method is used to analyze large data samples, the sampled major households are screened, and the statistical feature of the characteristic attribute that can effectively reflect the data filtration is determined. Sample regression analysis and adaptive processing on the sampling data are performed; the combined information fusion method implements the pattern identification of data filtration, and regression analysis is conducted according to the probability density of the detection statistic distribution in massive data environments; thus, data filtration according to the mode identification results. According to the above analysis, the overall structure of the probability mathematical model of data filtration is shown in Figure 1.

Fig. 1

According to the probability mathematical model shown in Figure 1, the mathematical information flow analysis of data filtration is performed, and the sample time series of the sampled data information stream is assumed. Y₁, Y₂, …, Y_N. Let A_j (L) for the fuzzy cluster center of the data probability statistics model, j = 1,2, …, k; the statistical regression analysis method was used, and the descriptive statistical analysis feature distribution matrix of massive data filtration was obtained from K=[K1TK2TK3TK4TK5T]T,L=[L1TL2TL3TL4TL5T]IK=\left[K_{1}^{T} K_{2}^{T} K_{3}^{T} K_{4}^{T} K_{5}^{T}\right]^{T}, L=\left[L_{1}^{T} L_{2}^{T} L_{3}^{T} L_{4}^{T} L_{5}^{T}\right]^{I}, M=[M1TM2TM3TM4TM5T]T, and W=[W1TW2TW3TW4TW5T]TM=\left[M_{1}^{T} M_{2}^{T} M_{3}^{T} M_{4}^{T} M_{5}^{T}\right]^{T}, \text { and } W=\left[W_{1}^{T} W_{2}^{T} W_{3}^{T} W_{4}^{T} W_{5}^{T}\right]^{T}, according to the above-described overall model design, using a descriptive statistical analysis method to construct a large data filtration statistical analysis model.

Data filtration statistical analysis in Leslie–Gower space is performed. The associated property rule analysis method is used, and the algorithm for data filtration is designed. The feature extraction algorithm for data filtration is described as follows.

On the basis of constructing a statistical characteristic analysis model for large data filtration, the optimization design of data filtering model is performed, and this paper proposes a data filtration method based on the probability mathematical model and gives data filtration probability density feature distribution mapping f : U × A → V in order to build data filtration in the phase space; the information function f (x, a) is the value on the element A in the resolution matrix, and the global registered gradient diversity method is used, and the core function of the data filter is X ⊂ U, the probability density is domain POSA∗⁡(X)\operatorname{POS}_{A}^{*}(X), the negative domain is NEGA∗⁡(X)\operatorname{NEG}_{A}^{*}(X); in the boundary arrest, the feature distribution set BNDA∗⁡(X)\operatorname{BND}_{A}^{*}(X) of massive data is obtained, whereby the fuzzy mathematical reasoning attribute set of data filtration is represented as follows: 4 POSA∗(X)=∪{E|P(X∣E)⟩P(X),E∈U/A} P O S_{A}^{*}(X)=\cup\{E|P(X \mid E)\rangle P(X), E \in U / A\} 5 NEGA∗(X)=∪{E|P(X∣E)⟩P(X),E∈U/A} N E G_{A}^{*}(X)=\cup\{E|P(X \mid E)\rangle P(X), E \in U / A\} 6 BDNA∗(X)=∪{E|P(X∣E)⟩P(X),E∈U/A} B D N_{A}^{*}(X)=\cup\{E|P(X \mid E)\rangle P(X), E \in U / A\}

In the formulas P(X∣E)=P(X)P(E)=card⁡(X∩E)card⁡(E),P(X)=card⁡(X)cadr⁡(U),card⁡(X)P(X \mid E)=\frac{P(X)}{P(E)}=\frac{\operatorname{card}(X \cap E)}{\operatorname{card}(E)}, P(X)=\frac{\operatorname{card}(X)}{\operatorname{cadr}(U)}, \operatorname{card}(X), indicating the probability density feature statistic in line data filtration [10].

The information entropy feature extraction is performed according to the association of the attribute. The scalar data time sequence attribute of data filtering is D_x = 2, and the regression analysis of the probability density distribution of the detection statistics in mass data is ξc1d2=35,ξc2d2=25,maxgc2(d2)=38,maxgc3(d2)=110.\xi_{c_{1}}^{d_{2}}=\frac{3}{5}, \xi_{c_{2}}^{d_{2}}=\frac{2}{5}, \max g_{c_{2}}\left(d_{2}\right)=\frac{3}{8}, \max g_{c_{3}}\left(d_{2}\right)=\frac{1}{10}.

Assuming that the decision threshold of X’s data filtering is D_x = 3, the reference component of the feature statistic of the data filtered is ξc1d3=1,ξc2d3=1,ξc3d3=1,maxgc1(d3)=74,maxgc2(d2)=38,maxgc3(d2)=74\xi_{c_{1}}^{d_{3}}=1, \xi_{c_{2}}^{d_{3}}=1, \xi_{c 3}^{d_{3}}=1, \max g_{c_{1}}\left(d_{3}\right)=\frac{7}{4}, \max g_{c_{2}}\left(d_{2}\right)=\frac{3}{8}, \max g_{c_{3}}\left(d_{2}\right)=\frac{7}{4}. According to the results of the decision statistical regression analysis, data filtration is achieved by the decision attribute identification method, and the filter output is as follows: ...

The probability mathematical model of data filtration is constructed using a fuzzy decision method, using a threshold test and threshold decision method, to achieve large data filtration, and the implementation process of the algorithm is as follows: