Category Archives: TI Nspire CX CAS

Visualizing operating characteristic curve with TI Nspire

In the study of quality control, sampling is an important technique to assess the overall quality level of a lot of production run. Operating characteristic curve is a great tool to understand the quality profile of acceptance sampling.

In TI Nspire, the OC curve can be defined as following using binomial distribution as an alternative to hypergeometric distribution.

oc-1

With the function defined, visualizing of 10% failure rate and sampling size of 20 can be done by graphing this function.

oc-2

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Visualizing Volatility Sensitivity in Delta hedged gains with TI Nspire

The TI Nspire calculator is a great platform for visualizing data via interactive graphs. The built-in facility like input slider for variable value adjustment allowed dynamic visualization to complex equations, like the volatility sensitivity in delta-hedged gains used financial investment. Since this strategy involved a single call option, the volatility exposure equals the vega value of the option.

The following setup on the Nspire provided the functions to calculate the vega values.
vega1

This spreadsheet input screen stores the spot prices and the calculated Black Scholes vega values.
vega2

Finally, with the data plotting screen the graph of Delta hedged gains of volatility sensitivity is completed. An additional slider control can easily be added on it to adjust an offset variable so as to visualize scenarios under different spot price.
vega3

Poisson prediction for soccer match odds

It is the World Cup season. There are many prediction models, and one of the most widely used statistical technique is the Poisson distribution:

soccer-poisson1

The historic match results are available in the public domain, for example, at http://eloratings.net/. The data are analysed to obtain an index referred to attack strength or goal expectancy. This can further elaborates into more complex data like home team and away team expectancy.

soccer-poisson2

By using a matrix of score scales, usually from 0 to 9, all possible outcomes under 10 goals per team are defined with the respective probability. An example matrix with scores from 0 to 2 will look like one below:

soccer-poisson3

This is the basics of predicting soccer in a quantitative way using the Poisson distribution. There are of course many other prediction methods and models, including organic method like asking the famous Paul the octopus 🙂

51% Blockchain attack

One of the predicted, and proved feasible, attack to the blockchain technology is the 51% attack. There are several forms of this attack including weakness in the blockchain algorithm itself that allowed easier than usual forking of chain to dishonestly win the popular vote mechanism. In other cases, the perpetrator has to amass more hashing power than all other nodes in the blockchain combined to corrupt the distributed ledger, and hence the name of “51%”.

An interesting mathematical study on the effectiveness of this attack is based on the regularized incomplete beta function to calculate the probability of success of a perpetrator.

incompletebeta