Launched Mobile app looking for investors


Well Established Agriculture Company looking for silent investor for acquisition funds


Luxury Online Leather Bags Seed Investment


T3 Endeavor Canada (British Columbia)


Looking for my Paul Allen


Loan Investment in Business


Kitty Door Knocker


Grand Medina Resort, Florida - 217 acre master planned development


Evotrux - The Fast, Easy Way to Book Freight & Trucks Online


Biomass Production Company Paying 15% Interest Annually


Constructing and Operating the Biggest Mushroom Farm in Quebec


Advanced Solar Power Collector


Forward Thinking Investor / Partner To Grow Natural Food Business to $10+ million


Invest in an up and coming Energy Beverage Company


Prospect Academy - Specialized Private Education


Consumer Packaged Goods - Hybrid Diapers – the first to reduce garbage.


Seeking funds to Buyout lone Investor


Environmental clean up


Affordable Housing


UPDATED **Canadian Made PPE Plant With 5 Year Government Contract


Passive Homes built at 50% of cost that sell for 20% more then any house. Done in 14 days on site


Virtual Reality Arcade Expansion


Share 10% of our sales profits on items you invest in plus minimum monthly payment


Self-Propelled Personal Flotation Device – US Patent 10,556,151


Real Business - $900,000/yr Sales


Home Care support Software solution


JUST THE BEST Delivery system for essential nutrients


Engine Oil Distribution


Travel Agency


Claystone Rental Property


Canada Esports Leader in Venues, Tournaments, and Content Creation.




Digital Asset Mining, Crypto Finance Start-Up, MVP Completed, 3 Year Profit Projections Ready


Audio Visual Solutions Company Opportunity


Stadium, bars, and restaurants application looking to raise funding for development and marketing


Osteoporosis Treatment


Hydrogen as a fuel source Technology - Time to Scale


JV OPPORTUNITY - 16%, 4 Months, Monthly Dist., 20% SP


Vancouver Real Estate and Healthcare


Funding for undertaking Research at Canadian University



Canadian Investment Network

Pitching Help Desk


"This is to inform you that I have already obtained all the investment funds that I need to launch my project. I thank you for doing all you have done for me. I am thrilled beyond measure. Apparently I have a better idea than even I knew."
Jerry Johnston - Mega Clean

 BLOG >> Recent

Estimating Probability Distributions: Part 1 [Business Models
Posted on July 11, 2013 @ 07:56:00 AM by Paul Meagher

In my previous blogs on modelling revenue for a season of lobster fishing I was fortunate in having data I could work with that allowed me to specify detailed probability distributions for the main revenue factors in my revenue model. I modelled the distribution of catch sizes with a normal distribution and the distribution of prices with a categorical distribution (I knew what the 4 price points were and roughly what their relative probabilities were). I was able to make some fairly strong assumptions about how the revenue factors (catch size in lbs and price per lb) in my revenue model were probabilistically distributed.

When a startup is trying to model their expected revenues for a forecast period, there is often more uncertainty regarding how the relevant factors in their revenue model might be distributed (these "relevant factors" can also be called "random variables"). In such cases, we may need to resort to modelling these random variables (e.g., monthly sales) with distributions that are easier to specify and take better account of our level of uncertainty.

In this blog I want to discuss 2 distributions that are useful in such situations: a uniform distribution and a triangular distribution.

If you need to forecast the level of sales over a forecast period but are new to the market place and are uncertain as to what the uptake of your product or service will be; or are uncertain about the level of production that you might be able to achieve (e.g., crop yield using a new growing technique), then you might want to consider using a uniform distribution to represent your level of sales. Why a uniform distribution? To specify the parameters for a uniform distribution, all you need to specify are the upper and lower bounds of that distribution (denoted a and b in the graph below). You assume that the actual level of sales can fall anywhere within that range with equal probability (i.e., 1/(b-a)). Specifying the upper and lower bounds for your level of sales is significantly easier than specifying the expected mean and standard deviation for, say, your monthly sales figures. Also, it can be argued that a uniform distribution better reflects your more extreme state of uncertainty with respect to the variable you are trying to predict; namely, your level of sales for each month or quarter in your forecast period.

Figure 1: Uniform Probability Distribution


If you have a bit more confidence about what your most likely level of sales might be, and also what the upper and lower bounds of your sales might be, then you should consider using a triangular distribution to represent your uncertainty about your level of sales. To specify the parameters for a triangular distribution, all you need to specify are three values: the lower bound, the upper bound, and the most likely value (or modal value). These values are denoted as a, b, and c respectively in the graph below. The probability of your most likely value is computed using the formula 2/(b-a).

Figure 2: Triangular Probability Distribution


My library of probability distribution functions includes a UniformDistribution.php object and a TriangleDistribution.php object that could be used to generate random values from these distributions, after you specify the relevant parameters to them. This means that even under conditions of extreme uncertainty regarding expected sales, you may still be able to model expected revenue, and expected variance in revenue, if you opt to model your revenue factors using a uniform or a triangular probability distribution. In my lobster fishing example, if I was more uncertain about the catch size or catch price to expect, I might opt to use a uniform or a triangular distribution to model the distribution of possible catch sizes and catch prices rather than the normal distribution and categorical distributions I chose because I had more data to go on.




 November 2020 [1]
 September 2020 [1]
 June 2020 [4]
 May 2020 [1]
 April 2020 [2]
 March 2020 [1]
 February 2020 [1]
 January 2020 [1]
 December 2019 [1]
 November 2019 [2]
 October 2019 [2]
 September 2019 [1]
 July 2019 [1]
 June 2019 [2]
 May 2019 [2]
 April 2019 [5]
 March 2019 [4]
 February 2019 [3]
 January 2019 [3]
 December 2018 [4]
 November 2018 [2]
 September 2018 [2]
 August 2018 [1]
 July 2018 [1]
 June 2018 [1]
 May 2018 [5]
 April 2018 [4]
 March 2018 [2]
 February 2018 [4]
 January 2018 [4]
 December 2017 [2]
 November 2017 [6]
 October 2017 [6]
 September 2017 [6]
 August 2017 [2]
 July 2017 [2]
 June 2017 [5]
 May 2017 [7]
 April 2017 [6]
 March 2017 [8]
 February 2017 [7]
 January 2017 [9]
 December 2016 [7]
 November 2016 [7]
 October 2016 [5]
 September 2016 [5]
 August 2016 [4]
 July 2016 [6]
 June 2016 [5]
 May 2016 [10]
 April 2016 [12]
 March 2016 [10]
 February 2016 [11]
 January 2016 [12]
 December 2015 [6]
 November 2015 [8]
 October 2015 [12]
 September 2015 [10]
 August 2015 [14]
 July 2015 [9]
 June 2015 [9]
 May 2015 [10]
 April 2015 [10]
 March 2015 [9]
 February 2015 [8]
 January 2015 [5]
 December 2014 [11]
 November 2014 [10]
 October 2014 [10]
 September 2014 [8]
 August 2014 [7]
 July 2014 [6]
 June 2014 [7]
 May 2014 [6]
 April 2014 [3]
 March 2014 [8]
 February 2014 [6]
 January 2014 [5]
 December 2013 [5]
 November 2013 [3]
 October 2013 [4]
 September 2013 [11]
 August 2013 [4]
 July 2013 [8]
 June 2013 [10]
 May 2013 [14]
 April 2013 [12]
 March 2013 [11]
 February 2013 [19]
 January 2013 [20]
 December 2012 [5]
 November 2012 [1]
 October 2012 [3]
 September 2012 [1]
 August 2012 [1]
 July 2012 [1]
 June 2012 [2]


 Agriculture [72]
 Bayesian Inference [14]
 Books [15]
 Business Models [24]
 Causal Inference [2]
 Creativity [7]
 Decision Making [15]
 Decision Trees [8]
 Design [37]
 Eco-Green [4]
 Economics [12]
 Education [10]
 Energy [0]
 Entrepreneurship [65]
 Events [2]
 Farming [20]
 Finance [25]
 Future [15]
 Growth [18]
 Investing [25]
 Lean Startup [10]
 Leisure [5]
 Lens Model [9]
 Making [1]
 Management [9]
 Motivation [3]
 Nature [22]
 Patents & Trademarks [1]
 Permaculture [36]
 Psychology [2]
 Real Estate [2]
 Robots [1]
 Selling [11]
 Site News [19]
 Startups [12]
 Statistics [3]
 Systems Thinking [3]
 Trends [7]
 Useful Links [3]
 Valuation [1]
 Venture Capital [5]
 Video [2]
 Writing [2]