Why you shouldn’t use the triangular distribution

The triangular distribution is popular in risk analysis because it seems to naturally embody the idea of ‘three point estimation’, where subjective judgement is used to estimate a minimum, a ‘best guess’ and a maximum value of a variable such as the cost of an item or the time taken to accomplish a task. It looks mathematically simpler than many of the standard distributions and could be regarded as the simplest probability density function that embodies a random variable with a given minimum, mode and maximum. Because of this, you may be tempted to think of it as the distribution that involves fewest assumptions and that it is therefore the one to use when you don’t know what the real distribution is. Its Wikipedia article says ‘… the triangle distribution has been called a “lack of knowledge” distribution’. Although the article gives no reference for this assertion, and I’ve never seen it explicitly stated anywhere else, it sounds plausible and I do think it represents the main reason people use the triangular distribution.

The problem with this idea is that it isn’t true. Read more

…another thing

On rereading my previous post, ‘Rebooting marine renewables’, it occurred to me that it is mostly about why the technologies need to be ‘rebooted’, and not about how it should be done. It was already too long by the time I got to that bit and I just wanted to finish it off as quickly as possible. I think, therefore, that it would be worthwhile expanding on this point, as it’s actually the most important part of the whole thing. Read more

Rebooting marine renewables

Last Monday evening (8 February) I watched an online broadcast of a lecture entitled ‘Marine Renewables – Crossing the Valley of Death’, given at the Institution of Civil Engineers in London by Clare Lavelle, who is head of energy consulting in Scotland for Arup. Before that Clare worked for Pelamis Wave Power and before that for Scottish Power on its wave and tidal projects. Her presentation was very much a statement of the standard wave and tidal narrative that if only the government would spend enough money the technology would succeed. She even name-checked Professor Salter’s conspiracy theory and the one about how the UK lost its world lead in wind energy to the Danes. Read more

A critique of anti-renewables rhetoric – part 1

These days more and more people seem to be railing against renewable energy—in the media, on the internet and down the pub. Here are some recent examples:

  • Wind farms ‘will never keep the lights on’: Study claims turbines are ‘expensive and deeply inefficient’ (Daily Mail, 27 October 2014). [Poulter, 2014]
  • Green energy costs ‘far higher than ministers admit’—report claims renewable energy is ‘the most expensive domestic policy disaster in modern British history’ (Daily Telegraph, 18 March 2015). [Gosden, 2015]
  • The windfarm delusion—The government has finally seen through the wind-farm scam – but why did it take them so long? (The Spectator, 3 March 2012). [Ridley, 2012]

This kind of stuff is common in the mainstream media, as the above examples testify. It often contains emotive terms like ‘disaster’ and ‘scam’, as the above examples also testify. The regular drip feed of it seems to be turning ‘Middle England’ against renewables and the government is responding by rolling back the measures it had in place to encourage them. However, I’ve yet to see a fact-based critique of these arguments anywhere. Here’s my attempt fill the gap.

Read more

VBA Monte Carlo risk analysis spreadsheet with correlation using the Iman-Conover method. Part 5

Welcome to the fifth and final part of my series of blog posts about how to build a VBA application in Microsoft Excel that performs Monte Carlo simulation. It follows on from my post on 11 February, which assembled into a working prototype the parts developed in earlier posts. (If you haven’t read any of the other posts in this series, it would probably be best to read those first, starting with Post 1.) Read more